Shipments of meat, meat by-products, and other ingredients are mixed together in

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Shipments of meat, meat by-products, and other ingredients are mixed together in several filling lines at a pet food canning factory. Management suspects that, although the average amount filled in the can of pet food is usually the same, the variability of the cans filled in Line A is much greater than that of Line B. The following sample data are obtained from filling 8-ounce cans. Assuming that the population variances are unequal, at the .05 level of significance, is there evidence of a difference between the average weights of cans filled on the two lines?

line a / line b 
8.005/7.997 x value
.012/.005 s value
11/16 N vale


a. If you use the 5% level of significance, what is the value of p? 
A) 2.09
B) .0586
C) .0038
D) .0293


b. What is the decision at the 5% level of significance? 
A) Fail to reject the null hypothesis: conclude that the lines are not different. 
B) Reject the null hypothesis and conclude the lines are different. 
C) Reject the alternate hypothesis and conclude Line A is different. 
D) Fail to reject the alternate hypothesis and conclude that both lines are different. 

 


c. This example is what type of test? 
A) One sample test of means. 
B) Two sample test of means. 
C) Paired t-test. 
D) Test of proportions. 

BSOP-326 Total Quality Management – Fujiyama Electronics Case Study – Due Week 7

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Fujiyama Electronics Case Study – Due Week 7

Objective | Project Deliverables | Grading Rubrics | Best Practices

 

Objective

This case study looks at the behavior of a circuit board process though the use of Control Charts. At least two Control Charts will need to be constructed, and from them you will be asked to provide an assessment of what you see. A template to facilitate the construction of the Control Charts has been provided. You are not required to use this template. A tutorial that outlines the steps for this case is located in Doc Sharing.

Problem Statement

Fujiyama Electronics, Inc. has had difficulties with circuit boards purchased from an outside supplier. Unacceptable variability occurs between two drilled holes that are supposed to be 5 cm apart on the circuit boards. Thirty samples of four boards each were taken from shipments from the supplier as shown in the data from the worksheet. Data in the worksheet below can also be assessed here.

pic

 

Project Deliverables

The student will submit the completed case study in a Word document to their Dropbox by the end of class Week 7. The paper is worth 50 points.

The student will complete and/or answer the following questions.

  1. Calculate X-Bar-Bar, R-Bar, and associated control limits using the data in the table above.
  2. Create X-Bar•R (Average & Range) Control Charts from the data in the table above.
  3. Discuss notable out-of-control conditions displayed in the completed X-Bar•R (Average & Range) Control Charts. Only consider points outside the control limits. Do not consider runs, set of points within certain zones, etc.
  4. If the conditions you note could be defined as assignable conditions and they are removed from the process, what will happen to the X-Bar•R Control Chart?

(a) Remove the data related to the out-of-control points you observed from the origainal data and recalculate a new X-Bar-Bar, R-Bar, and associated control limits.
(b) Create new X-Bar•R (Average & Range) Control Charts from your updated data.

  1. Discuss how the two sets of Control Charts are different. What has changed?

The format of the case study should conform to the Publication Manual for the American Psychological Association (APA), 6th edition, for title page and text. Citations and references are not required. A basic APA tutorial can be found inthe Webliography and a paper template can be found in Doc Sharing. The completed case study will be submitted to your Dropbox as an MS Word document. All graphics and charts will be a part of the Word document and submitted as a file. Documents authored in other applications such as WordPerfect or MS Works will not be accepted.

This project is to be accomplished individually, and will reflect the work of each student. All DeVry University policies are in effect including the plagiarism policy. Late papers will not be accepted without prior permission.

Submit your Fujiyama Case Study paper to the Dropbox located on the silver tab at the top of this page by the end of Week 7. For instructions on how to use the Dropbox, read these Step-by-Step Instructions or watch this Tutorial iconDropbox Tutorial.

See Syllabus section “Due Dates for Assignments & Exams” for due date information.

 

Grading Rubrics

 

First Control Chart (40 Percent)

Points Possible

Points Earned

Comments

All calculations are correct.

5

    

X-Bar & R charts are presented and correct.

5

    

All conditions of importance discussed.

10

    

Total

20

    

Second Control Chart (40 Percent)

Points Possible

Points Earned

Comments

All calculations are correct.

5

    

X-Bar & R charts are presented and correct.

5

    

Differences between the two sets of Control Charts are thoroughly discussed.

10

    

Total

20

    

Mechanics (20 Percent)

Points Possible

Points Earned

Comments:

The paper, including the title page follows APA guidelines for format. (References and citations not required)

2

    

Sentences are complete, clear, and concise.

2

    

The paper is laid out with effective use of headings, font styles, and white space.

2

    

Rules of grammar, usage, and punctuation are followed.

2

    

Spelling is correct.

2

    

Total

10

    

Total (100 Percent)

Points Possible

Points Earned

Comments:
 

50

    

 

 

Best Practices

xx

The following are the best practices in preparing this paper. Sample papers, using the APA format, are located in Doc Sharing. Other useful information has also been provided there, including an APA paper template.

  • Cover Page – Include who you prepared the paper for, who prepared it, and the date.
  • Body of Your Work – Titles to identify different areas that you address. State the main ideas, major points in each idea, and supporting information. Break down each main idea you will use in the body of your paper. Show some type of division like separate sections that are labeled, separate groups of paragraphs, or headers. You would include the information you found during your research and investigation.
  • Summary and Conclusion – Summarizing is similar to paraphrasing but presents the gist of the material in fewer words than the original. An effective summary identifies the main ideas and major support points from the body of your work. Minor details are left out.
    Additional hints on preparing the best possible project.
    • Apply a three-step process of writing… Plan, Write, and Complete.
    • Prepare an outline of your research paper before you go forward.
    • Complete a first draft and then go back to edit, evaluate, and make any changes required.
    • Use visual communication if it will help clarify and support your work. Any material that can be removed and not affect the clarity of your work is essentially filler, and should be avoided. Filler distracts from the flow of your work and will most likely cause you to lose points.
  • References – Not required for this case study.

 

1. Dolly has seven books from the Statistics is Fun series. She plans on bringing three of the seven books with her in a road trip. How many different ways can the three books be selected? 2. Questions 2. involves the random variable x with probability

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1. Dolly has seven books from the Statistics is Fun series. She plans on bringing three of the seven books with her in a road trip. How many different ways can the three books be selected? 

 

2. Questions 2. involves the random variable x with probability distribution given below.

Show all work. Just the answer, without supporting work, will receive no credit.

x

-1

0

1

2

P(x)

0.1

0.3

0.4

0.2

 

 

 

 – Determine the expected value of x. 

– Determine the standard deviation of x. (Round the answer to two decimal places) 

 

 

3. The heights of walnut trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.

– What is the probability that a randomly selected walnut tree is greater than 12 feet? 

– Find the 75th percentile of the walnut tree height distribution. 

– If a random sample of 36 walnut trees is selected, what is the probability that the mean height of this sample is less than 10 feet? 

 

4. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will receive no credit.  

 

5. Given a sample size of 100, with sample mean 730 and sample standard deviation 100, we perform the following hypothesis test at the 0.05 level.

 H0:=750

H1: 750

– Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

– Determine the critical values. Show all work; writing the correct critical value,

without supporting work, will receive no credit.

–        What is your conclusion of the test? Please explain.  

 

26. Consider the hypothesis test given by

 H0:p=0.5

H1:p<0.5

 

In a random sample of 225 subjects, the sample proportion is found to be

P(hut)=0.51.

 

–        Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.  

–         

– Determine the P-value for this test. Show all work; writing the correct P-value,

without supporting work, will receive no credit.

–        Is there sufficient evidence to justify the rejection of

H0 at the =0.01 level? Explain.

 

 

 7. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words. Each was asked to list as many of the words as he or she could remember both 1 hour and 24 hours later. The result is shown in the following table.

 

Number of words recalled

 

subject

1 hour later

2 hour later

1

14

12

2

18

15

3

11

9

4

13

12

5

12

12

 

 

Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours?

Assume we want to use a 0.01 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the critical value. Show all work; writing the correct critical value,

without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that the mean number of words

recalled after 1 hour exceeds the mean recall after 24 hours? Justify your conclusion.

 

Refer to the following data for Questions  8 and 9.

 

x

0

-1

3

5

y

3

-2

3

8

 

 

 8. Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.  

 9. Based on the equation from #  8, what is the predicted value of y if x = 4? Show all work and justify your answer.  

 

10. The store sells four different types of teddy bears. The manager reports that the four types are equally popular. Suppose that a sample of 100 purchases yields observed counts 30, 24, 22, and 24 for types 1, 2, 3, and 4, respectively.

 

type

1

2

3

4

number

30

24

22

24

 

Assume we want to use a 0.10 significance level to test the claim that the four types are equally popular.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the critical value. Show all work; writing the correct critical value,

without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the manager’s claim that the four types are equally popular? Justify your answer.

Results from previous studies showed 79% of all high school seniors from a certain city plan to attend

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1. Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance. 

State the null and alternative hypotheses.

A.H0: p ≤ .79, H1: p > .79
B.H0: p = .79, H1: p ≠ .79
C.H0: = .79, H1: > .79
D.H0: μ = .79, H1: μ > .79

2. A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy?

Compute the value of the appropriate test statistic.

A.Chi-sq = 27.50
B.z = 1.65
C.t = 27.50
D. = 30.58

3. A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy?

State the null and alternative hypotheses. 

A.H0: σ2 ≠ 1.2, H1: σ2 = 1.2
B.H0: σ2 < 1.2, H1: σ2 ≠ 1.2
C.H0: σ2 ≤ 1.2, H1: σ2 > 1.2
D.H0: σ2 ≥ 1.2, H1: σ2 ≠ 1.2

4. Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

What is the p-value associated with your test of hypothesis?

A.0.2437
B.0.6874
C.0.7563
D.0.4874

5. 
The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization’s staff of salespersons. He believes that the proportion of women in similar sales positions across the country is less than 45%. Hoping to find support for his belief, he directs you to test 

H0: p ≥ .45 vs H1: p < .45.

In doing so, you collect a random sample of 50 salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women.

Compute the test value that you would use in conducting this test. Place your answer, rounded to 3 decimal places, in the blank. For example, -2.345 would be a legitimate entry. 

5. The ABC battery company claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company’s claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below. 

Test of H0: >= 100 versus H1: < 100 
Sample mean 98.5 
Std error of mean 0.777 

Assuming the life length of batteries is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, 0.0234 would be a legitimate entry. 

6. A medical doctor wishes to test the claim that the standard deviation of the systolic blood pressure of deep sea divers is less than 450. To do so, she selected a random sample of 20 divers and found s = 432. 

Assuming that the systolic blood pressures of deep sea divers are normally distributed, if the doctor wanted to test her research hypothesis at the .01 level of significance, what is the critical value? 

Place your answer, rounded to 3 decimal places, in the blank. For example, 4.567 would be a legitimate entry.

7. Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample of n = 25 light bulbs and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below. 

Test of H0: ≤ 1500 versus H1: > 1500 
Sample mean 1509.5 
Std error of mean 4.854

Assuming the life length of this type of lightbulb is normally distributed, if you wish to conduct this test using a .05 level of significance, what is the critical value that you should use? Place your answer, rounded to 3 decimal places in the blank. For example, 1.234 would be a legitimate entry. 

GOOGLE STOCK QUESTION (2015 VERSION)

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Project 3 instructions

 

Based on Larson & Farber: sections 5.2-5.3

To obtain the data:

 

  1. Go to this website.
  2. Set the date range to be 1/2/2014 to 1/2/2015.
  3. Click “update”. 
  4. Click the link on the right that says Download to Spreadsheet

 

This project will only use the Closing Values. Assume that the closing prices of the stock form a normally distributed data set. This means that you need to use Excel to find the mean and standard deviation and then use those numbers and the methods you learned in sections 5.2 and 5.3 of our text book for Normal distributions to answer the questions.

 

Complete this assignment within a single Excel file. Show your work or explain how you obtained each of your answers.  Answers with no work and no explanation will receive no credit.

 

1.      If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? Hint: You do not want to calculate the mean to answer this one. The probability would be the same for any normal distribution. (5 points)

 

 

 

2.      If a person bought one share of Google stock within the last year, what is the probability that the stock on that day closed at more than $550? (5 points)

 

3.      If a person bought 1 share of Google stock within the last year, what is the probability that the stock on that day closed within $45 of the mean for that year? (5 points)

 

 

 

4.      Suppose a person within the last year claimed to have bought Google stock at closing at $500 per share. Would such a price be considered unusual?  Be sure to use the definition of unusual from our textbook. (5 points)

 

 

5.      At what prices would Google have to close at in order for it to be considered statistically unusual? You should have a low and high value. ?  Be sure to use the definition of unusual from our textbook. (5 points)

 

6.      What are Quartile 1, Quartile 2, and Quartile 3 in this data set? Use Excel to find these values.  This is the only question that you should answer without using anything about the Normal distribution. (5 points)

 

7.       Is the normality assumption that was made at the beginning valid? Why or why not? Hint: Does this distribution have the properties of a normal distribution as described in our textbook? It does not need to be perfect.  Real data sets are never perfect.  However, it should be close. One option would be to construct a histogram like we did in Project 1 and see if it has the right shape.  If you go this route, something in the range of 10 to 12 classes would be a good number. (5 points)

 

 

 

 

 

Correct mean: 1.5 points

Correct SD: 1.5 points

Correct date range: 2 point

 

 

Submit your work through the assignment link by 11:59 p.m. (ET) on Monday, 2/16.Please make sure to show all steps. If you use Excel to help find the answer, explain in words what you do.  Note that you must do this project on your own—you may not work with other students. You are always welcome to ask your instructor for help.

 

Data Manipulation

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In this project, you will be assigned the task to record money received for a school fundraiser and create an Excel spreadsheet to record your receipts.
  • You will determine the funds received and use the text to column feature (concatenate, apply conditional formatting, sort and filter data).
  • You will determine your analysis and use sorting and filtering data, conditional formatting, as well as subtotals.
To complete the assignment, perform the following steps:
  1. Open this Excel workbook titled “Fundraiser Receipt” and save the worksheet as “FirstInital_LastName_School expenses.xlsx.”
  2. 2. Add a column to the right of the “Last Name” column and name as “Full Name” Use the Concatenate function to join First Name and Last Name together split by a space.
    • Click here for more information on how to use the concatenate function.
  3. Sort Columns C (C2:C21), using A–Z formatting.
  4. 4. Using the Conditional Formatting, determine which students have provided over $50 for the fundraiser in Funds Received Column and also in Funds Pending Column.
    • The conditional formatting function allows you to apply different formatting options to data that meets certain conditions.
    • Click here for more information on how to use the conditional formatting function.
  5. 5. Click on any cell in (A1:E22), and apply a design to your data: In the Styles group, select Format as Table and use a dark formatting option.
  6. 6. At Total row (E22 and F22), provide a Sum for the Funds Raised and Funds Pending.
  7. Add the Title “College Fundraiser Project” by inserting blank lines. Change the font size of the title to 22, fill color with white background, darker 35%.
  8. Change the orientation to landscape.
  9. Name the worksheet “Fundraiser_Receipt_Solution.”
  10. Save the workbook. Close the workbook and then exit Excel. Submit your Excel spreadsheet.

References

Microsoft. (n.d.). Concatenate function. Retrieved from http://office.microsoft.com/en-us/starter-help/concatenate-function-HP010342288.aspx?CTT=3

Microsoft. (n.d.). Quick start: Apply conditional formatting. Retrieved from http://office.microsoft.com/en-us/excel-help/quick-start-apply-conditional-formatting-HA010370614.aspx

 

https://support.office.com/en-us/article/CONCATENATE-function-8f8ae884-2ca8-4f7a-b093-75d702bea31d?CTT=3&CorrelationId=75a54de3-74bc-46f2-a5b7-ace48b479e91&ui=en-US&rs=en-US&ad=US&fromAR=1

 

https://support.office.com/en-us/article/Quick-start-Apply-conditional-formatting-6b6f7c2a-5d62-45a1-8f67-584a76776d67?CorrelationId=16086d23-9dce-4ab9-b544-368bd294c49e&ui=en-US&rs=en-US&ad=US&ocmsassetID=HA010370614

Concerning DMAIC

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1. Concerning DMAIC,
a. DMAIC is a unique process for problem solving
b. DMAIC is a unique Six Sigma system for eliminating process variation
c. DMAIC has similarities to 8-D and PDCA
d. DMAIC is an 8-step problem solving Six Sigma approach for reducing defects

2. Cpk would typically be used in the D stage of DMAIC.
a. True
b. False

3. Another name for the Logic Tree is the Step Chart.
a. True
b. False

4. The last step in DMAIC has would include 
a. Documentation including engineering drawings
b. Work instructions and standard operating procedures.
c. Policies and time fence rules
d. All of the above answers

5. The validation of the objective of the project using DMAIC would happen typically in the D or Define step of DMAIC.
a. True
b. False

6. Mapping is a helpful tool in DMAIC and would often be applied in the D and A steps.
a. True
b. False

7. In Six Sigma, the voice of the customer is
a. Not always obvious to the suppliers and can be quite different than interpreted.
b. Is usually communicated completely and formally with drawings or specifications.
c. Is seldom at the root of customer dissatisfaction.
d. All of the above answers.

8. Solutions confirmed in DMAIC are often applicable to other facilities in the company and should be optimized by implementing solutions in other applications within the organization after the final step.
a. True
b. False

9. The SIPOC would be utilized in the following applications
a. almost every problem solving opportunity using DMAIC
b. in supply chain applications mostly such as with supplier fidelity issues using DMAIC
c. mostly in DMIAC applications where customers are exchanging money for goods or services from a supplier
d. b and c

10. Stakeholder Analysis includes analysis and actions to change support levels and opinions of people involved with the process being improved through DMAIC.
a. True
b. False

comment tania

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 I NEED A POSITIVE COMMENT BASED IN THIS ARGUMENT.. BETWEEN 150-200 WORDS

 

Measuring each single piece of item can sometimes be unpractical, and that is why statistical methods of solving problems were developed. A sample of the population being measured can be more practical (Taeger & Kuhnt, 2014). T-test and T-test are some of the known statistical hypothesis testing methods that have been developed.
 A T-test is a method of hypothesis testing that uses a student’s T-distribution when the null hypothesis is true. A T-test is used in testing the mean of a population against a standard or comparing two population means when the standard deviation is not known, and the sample is limited (n<30). The method is easy to use, flexible, adaptable to various circumstances and straightforward (Park, 2015).

 A Z-test is used to test the mean of a population versus a standard or to compare two populations’ means with samples that are large (n≥30), whether the standard deviation of the population is known or not (Taeger & Kuhnt, 2014).A Z-test determines the probability that a new set of data will be near the point that a certain score was calculated.
 A Z-test is usually appropriate over a T-test when the standard deviation of a population is known and when there is a normal distribution. Also, a Z-test is more appropriate when comparing the mean of a sample and a population to know if there is a substantial difference between them. There are fluctuations that can occur in a T-test when using large sample variances and would not be experienced when using the Z-test. For instance, a Z-test would be preferable when comparing the average salaries of male engineers and female engineers (Park, 2015).

  
 References
Park, H. M. (2015). Hypothesis testing and statistical power of a test. 
Taeger, D., & Kuhnt, S. (2014). Statistical hypothesis testing. Statistical Hypothesis Testing with SAS and R, 3-16.

 

 

 
                                

 

Linear Programming Class

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I have a linear programming class that requires Lindo solver outputs. Can anyone assist me in this class. The following is a example problem.

 

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers 

   
have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge  
different prices for the components. Component price data (in price per unit) are as follows:      
                       
    Supplier                  
Component 1 2 3 Production              
1 $12 $13 $14 1,000              
2 $10 $11 $10 800              
Capacity 600 1000 800                
                       
                       
Each supplier has a limited capacity in terms of the total number of components it can supply.  However, as long   
as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component  
2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier  
capacities and Edwards’ production plan are given above.            

If the Edwards production plan for the next period includes 1000 units of component 1 and 800 units component 2. How many units of each component should be ordered from each supplier? What is the total purchased cost for the components?

Create the entire linear programming model below and plug into LINDO and interpret the results.

Statistics – Purchase below!

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Question 1 (3 points)
 
The standard normal distribution has a mean of a standard deviation respectively equal to
Question 1 options:
 1 and 1
 0 and 0
 1 and 0
 0 and 1
________________________________________
Question 2 (3 points)
 
Given that Z is a standard normal variable, the value z for which P(Z  z) = 0.2580 is
Question 2 options:
 
0.242
 -0.65
 0.70
 0.758
________________________________________
Question 3 (3 points)
 
The result of tossing a coin once will be either head or tail. Let A and B be the events of observing head and tail, respectively. The events A and B are:
Question 3 options:
 
conditional
 mutually exclusive
 unilateral
 independent
________________________________________
Question 4 (3 points)
 
Which of the following statements are true?
Question 4 options:
 
Probabilities must be nonnegative.
 Probabilities can either be positive or negative.
 Probabilities can be any positive value.
 Probabilities must be negative.
________________________________________
Question 5 (3 points)
 
If P(A) = P(A|B), then events A and B are said to be
Question 5 options:
 
mutually exclusive
 complementary
 independent
 exhaustive
________________________________________
Question 6 (3 points)
 
 The joint probabilities shown in a table with two rows, A1and A2 and two columns, B1 and B2, are as follows: P(A1 and B1) = .10, P(A1 and B2) = .30, P(A2 and B1) = .05, and P(A2 and B2) = .55. Then P(A1|B1), calculated up to two decimals, is
Question 6 options:
 
.65
 .67
 .33
 .35
________________________________________
Question 7 (3 points)
 
There are two types of random variables, they are
Question 7 options:
 
discrete and continuous
 exhaustive and mutually exclusive
 complementary and cumulative
 real and unreal
________________________________________
Question 8 (3 points)
 
If A and B are any two events with P(A) = .8 and P(B| ) = .7, then P( and B) is
Question 8 options:
 
.56
 .14
 .24
 None of the above
________________________________________
Question 9 (3 points)
 
Which of the following best describes the concept of marginal probability?
Question 9 options:
 
It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs.
 It is a measure of the likelihood that a particular event will occur, given that another event has already occurred.
 It is a measure of the likelihood of the simultaneous occurrence of two or more events.
 None of the above.
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Question 10 (3 points)
 
We assume that the outcomes of successive trials in a binomial experiment are:
Question 10 options:
 
identical from trial to trial
 probabilistically independent
 probabilistically dependent
 random number between 0 and 1
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Question 11 (3 points)
 
The mean of a binomial distribution with parameters n and p is given by:
Question 11 options:
 
np
 n – p
 n + p
 n/p
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Question 12 (3 points)
 
The mean  of a probability distribution is a:
Question 12 options:
 
measure of skewness of the distribution
 measure of variability of the distribution
 measure of relative likelihood
 measure of central location
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Question 13 (3 points)
 
If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?
Question 13 options:
 
equal to the mean
 to the left of the mean
 to the right of the mean
 None of the above
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Question 14 (3 points)
 
The standard deviation  of a probability distribution must be:
Question 14 options:
 
a nonnegative number
 a negative number
 a number between 0 and 1
 All of the above
 None of the above
 
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Question 15 (5 points)
 
Consider a random variable X with the following probability distribution:
P(X=0) = 0.25, P(X=1) = 0.35, P(X=2) = 0.15, P(X=3) = 0.10, and P(X=4) = 0.15.
Find the mean and standard deviation of X.
Question 15 options:
Mean = 1.5500
Standard deviation = 1.3592
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Question 16 (3 points)
 
Consider a random variable X with the following probability distribution:
P(X=0) = 0.08, P(X=1) = 0.22, P(X=2) = 0.25, P(X=3) = 0.25, P(X=4) = 0.15, P(X=5) = 0.05
Find P(2<X<4)

Question 16 options:
  ________________________________________
Question 17 (3 points)
 
Suppose that 20% of the students of Big Rapids High School play sports. Moreover, assume that 55% of all students are female, and 15% of all female students play sports.
 
If we choose a student at random from this school, what is the probability that this student is a female who does not play sports?

Question 17 options:
  _______________________________________
Question 18 (4 points)
 
Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam. For what range of scores should a “C” grade be given?
Question 18 options:

  ________________________________________
Question 19 (4 points)
 
The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold.

What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?
Question 19 options:
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Question 20 (3 points)
 
A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend $20 or more at this store?
Question 20 options:

Question 21 (3 points)
 
A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend exactly $28 at this store?
Question 21 options:
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Question 22 (3 points)
 
If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to
Question 22 options:
 
10
 30
 90
 13
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Question 23 (2 points)
 
Suppose A and B are mutually exclusive events where P(A) = 0.2 and P(B) = 0.5, then P(A or B) = 0.70.
Question 23 options:
 
True
 False
Question 24 (2 points)
 
If A and B are two independent events with P(A) = 0.20 and P(B) = 0.60, then P(A and B) = 0.80
Question 24 options:
 
True
 False
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Question 25 (2 points)
 
The number of homeless people in Boston is an example of a discrete random variable.
Question 25 options:
 
True
 False
Question 26 (2 points)
 
The multiplication rule for two events A and B is: P(A and B) = P(A|B)P(A).
Question 26 options:
 
True
 False
Question 27 (2 points)
 
If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive.
Question 27 options:
 
True
 False
Question 28 (2 points)
 
Probability is a number between 0 and 1, inclusive, which measures the likelihood that some event will occur.
Question 28 options:
 
True
 False
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Question 29 (2 points)
 
The left half under the normal curve is slightly smaller than the right half.
Question 29 options:
 
True
 False
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Question 30 (2 points)
 
If X is a binomial random variable with n = 20, and p = 0.30, then P(X = 10) = 0.50.
Question 30 options:
 
True
 False
Question 31 (2 points)
 
The binomial random variable represents the number of successes that occur in a specific period of time.
Question 31 options:
 
True
 False
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Question 32 (2 points)
 
Using the standard normal curve, the Z- score representing the 99th percentile is 2.326.
Question 32 options:
 
True
 False
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Question 33 (2 points)
 
Using the standard normal curve, the Z- score representing the 75th percentile is 0.674.
Question 33 options:
 
True
 False
Question 34 (2 points)
 
A random variable X is normally distributed with a mean of 175 and a standard deviation of 50. Given that X = 150, its corresponding Z- score is –0.50.
Question 34 options:
 
True
 False
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Question 35 (3 points)
 
In a particular community, there are medical doctors in 40% of the households. If a household is chosen at random from this community, what is the probability that there is not a medical doctor in this household?
 
Question 35 options:
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Question 36 (3 points)
 
Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 9 pounds and a standard deviation of 3 pounds.
What proportion of the dieters lost more than 12 pounds?