week 7 quiz

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1.

Let .

Are the events F and G mutually exclusive?

2.

Let .

Are the events F and G complementary?

3.

Let

be a sample space of an experiment with outcomes

. List all the events of this experiment.

4.
An experiment consists of selecting a card from a standard deck of playing cards and noting whether the card is black (B) or red (R). Describe an appropriate sample space for this experiment.
5.
An experiment consists of selecting a card from a standard deck of playing cards and noting whether the card is black (B) or red (R). What are the events of this experiment?
6.
An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event “A head is tossed and an odd number is rolled.”

7.
A sample of two transistors taken from a local electronics store was examined to determine whether the transistors were defective (d) or nondefective (n). What is an appropriate sample space for this experiment?

8.
In a television game show, the winner is asked to select three prizes from five different prizes, A, B, C, D, and E. Describing a sample space of possible outcomes (order is not important) determine the number of points there are in the sample space corresponding to a selection that includes A.

9.
As part of a quality-control procedure, an inspector at Bristol Farms randomly selects ten eggs from each consignment of eggs he receives and records the number of broken eggs. Describe the event F that at least nine eggs are broken.

10.

Let be a sample space associated with an experiment.

How many subsets of contain either the number 5 or the number 6?

11.

The following breakdown of a total of 18,686 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT).

Mode of Transportation

Car

Train

Bicycle

Plane

Number of Fatalities

16,525

842

698

538

What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a train or a plane accident? Round answer to two decimal places.

12.

In a survey of 900 likely voters, the following question was asked: Do you support using cameras to identify red-light runners? The results of the survey follow:

Answer

Strongly support

Somewhat support

Somewhat oppose

Strongly Oppose

Don’t know

Respondents

410

212

95

164

19

What is the probability that a person in the survey selected at random favors using cameras to identify red-light runners?

13.

According to Mediamark Research, 88 million out of 179 million adults in the United States correct their vision by using prescription eyeglasses, bifocals, or contact lenses. (Some respondents use more than one type.) What is the probability that an adult selected at random from the adult population uses corrective lenses? Round your answer to the nearest thousandth.

14.
One light bulb is selected at random from a lot of 110 light bulbs, of which 2% are defective. What is the probability that the light bulb selected is defective?

15.
If a ball is selected at random from an urn containing two red balls, three white balls, and five blue balls, what is the probability that it will be a white ball?

16.
What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec?

17.

The grade distribution for a certain class is shown in the table.

Grade

A

B

C

D

F

Frequency of Occurrence

6

6

18

8

2

What is the probability that a student selected at random from this class received a passing grade (D or better)?

18.
In a sweepstakes sponsored by Gemini Paper Products, 100,000 entries have been received. If 2 grand prize, 10 first prizes, 35 second prizes, and 600 third prizes are to be awarded, what is the probability that a person who has submitted one entry will win a prize?

19.

In a survey conducted in 2007 of 954 adults 18 years old and older, the following question was asked: How are American companies doing on protecting the environment compared with companies in other countries? The results are summarized below:

Answer

Behind

Equal

Ahead

Don’t know

Respondents

382

236

240

96

If an adult in the survey selected at random, what is the probability that he or she said that American companies are equal or ahead on protecting the environment compared with companies in other countries? Round your answer to two decimal places.

20.
A study conducted by the Corrections Department of a certain state revealed that 163,767 people out of a total adult population of 1,799,738 were under correctional supervision (on probation, parole, or in jail). What is the probability that a person selected at random from the adult population in that state is under correctional supervision?

Children in the United States account directly for $36 billion in sales annually. When their indirect influence over product decisions from stereos to vacations is considered, the total economic spending affected by children in the United States is $2

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Question 9.48

Children in the United States account directly for

$36 billion in sales annually. When their indirect influence

over product decisions from stereos to vacations is considered,

the total economic spending affected by children in the

United States is $290 billion. It is estimated that by age 10.

a child makes an average of more than five trips a week to a

store (data extracted from M. E. Goldberg, G. 1. Gorn, L. A.

Peracchio, and G. Bamossy, “Understanding Materialism

Among Youth,” Journal of ConSlimer Psychology, 2003.

13(3), pp. 278-288). Suppose that you want to prove that

children in your city average more than five trips a week to

a store. Let fL represent the population mean number of

times children in your city make trips to a store.

a. State the null and alternative hypotheses.

b. Explain the meaning of the Type I and Type II errors in

the context of this scenario.

c. Suppose that you carry out a similar study in the city in

which you live. You take a sample of ) 00 children and find that the mean number of trips to the store is 5.47 and the sample SD of the number of trips to store is 1.6. At the 0.01 level of significance, is there evidence that the population mean number of trips to the store is greater than 5 per week?

 

d) Interpret the meaning of the p- value in (c )

 

Math

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 I have a homework 

 

 

A manufacturer produces bolts of a fabric with a fixed width. A quantity q of this fabric (measured in yards) that is sold is a function of the selling price p (in dollars per yard), so we can write q=f(p). Then, the total revenue earned with selling price p is R(p)=pf(p). 

Find R′(30), given f(30)=12000, and f′(30)=−450. (What does this mean?) 

 

 

R′(30)=?

R′(30)=

MATH

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Chi-square distribution

Find the median of the chi-square distribution with 22degrees of freedom. Round your answer to at least two decimal places

In the question above the resolution had the equation of P(Xsquare > M)=0.5. Where did the 0.5 come from? Is it coming from the previous question answer?

 

 

 

Chi-square distribution

Use the calculator provided to solve the following problems.

  • Suppose that  follows a chi-square distribution with  degrees of freedom. Compute . Round your answer to at least three decimal places.

     

  • Suppose again that  follows a chi-square distribution with  degrees of freedom. Find  such that . Round your answer to at least two decimal places.

     

  • Find the median of the chi-square distribution with  degrees of freedom. Round your answer to at least two decimal places.

 

 

Additional Resources
Elementary Statistics (A Brief Version), 6th Ed.
Bluman
Chapter 7: Confidence Intervals and Sample Size
Section 7.4: Confidence Intervals for Variances and Standard Deviations
 

  • We’re asked to compute , where  follows a chi-square distribution with  degrees of freedom. Using the calculator, we can compute  and use the complement rule to obtain :
     
      .

    (Note that, since the degrees of freedom in the above calculation must be specified for the ALEKS calculator, the expression  appears as  with  in the calculator input.)

     

     

  •  
     Figure 1
     

    We are asked to find  such that  for a chi-square distribution with degrees of freedom. Note that such a  is the value that cuts off an area of  in the right tail of this distribution, that is,  for the distribution. See Figure 1, which depicts the distribution and an area of  shaded to the right of .

    Using the calculator, we get

     
      .

    (Note that we have to use the input  to specify the degrees of freedom.)

     

  • We’re asked to find the median of the chi-square distribution with  degrees of freedom. The median of a continuous distribution is the value that divides the distribution in half; in other words, the probability of obtaining a value greater than the median is  and the probability of obtaining a value less than the median is .
    In finding the median of the chi-square distribution with  degrees of freedom, then, we are finding the value such that , where  follows a chi-square distribution with  degrees of freedom. In other words, we are finding  . Using the calculator, we get

    .

The answer is:



Median

Mathematics

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Q2.(64-Ch3)64. Marginal Analysis Suppose the profit (in cents) from selling    x lb of potatoes is given by P(X)=15x+25x2

 

1. Find the average rate of change in profit from selling each of the following amounts.

a. 6 lb to 7 lb              b. 6 lb to 6.5 lb           c. 6 lb to 6.1 lb

 

Find the marginal profit (that is, the instantaneous rate of change of the profit) from selling the following amounts.

d. 6 lb          e. 20 lb         f. 30 lb

 

g. What is the domain of x?

 

h. Is it possible for the marginal profit to be negative here? What does this mean?

 

i. Find the average profit function. (Recall that average profit is given by total profit divided by the number produced, or

P( x ) = P( x ) / x)

 

j. Find the marginal average profit function (that is, the function giving the instantaneous rate of change of the average profit function).

 

k. Is it possible for the marginal average profit to vary here? What does this mean?

 

l. Discuss whether this function describes a realistic situation.

 

 

Q3. (58-4.1)58. Money The total amount of money in circulation for the years 1950–2009 can be closely approximated by 

 

M(t)=  0.005209t3  – 2 0.04159t2 – 2 0.3664t + 34.49

 

1. where  t  represents the number of years since 1950 and M( t ) is in billions of dollars. Find the derivative of M( t ) and use it to find the rate of change of money in circulation in the following years. Source: U.S. Treasury.

 

a. 1960      b. 1980     c. 1990      d. 2000

 

e. What do your answers to parts a–d tell you about the amount of money in circulation in those years?

 

Q4. (62-4.1)62.Brain Mass The brain mass of a human fetus during the last trimester can be accurately estimated from the circumference of the head by   M ( c ) = c3 /100 – 1500/c,

 

     

Where m( c)  is the mass of the brain (in grams) and c is the circumference (in centimeters) of the head. Source: Early Human Development.

 

a. Estimate the brain mass of a fetus that has a head circumference of 30 cm.

b. Find the rate of change of the brain mass for a fetus that has a head circumference of 30 cm and interpret your results.

 

Q5.(72-4.1)72.Velocity If a rock is dropped from a 144-ft building, its position (in feet above the ground) is given by

 

S( t ) = -16t2 + 144,

where t is the time in seconds since it was dropped.

 

a. What is its velocity 1 second after being dropped? 2 seconds after being dropped?

 

b. When will it hit the ground?

 

c. What is its velocity upon impact?

 

Q6.(48-4.2)48. Muscle Reaction When a certain drug is injected into a muscle,the muscle responds by contracting. The amount of contraction, s (in millimeters) is related to the concentration of the drug,  x (in milliliters) by s( x ) = x / m+nx

 

 

Where m and n are constants.

a. Find s’( x )

b. Find the rate of contraction when the concentration of the drug is 50ml, m =10, and n = 3.

 

 

 

 

 

 

 

 

 

Q7.(52-4.2) 52. Optimal Foraging Using data collected by zoologist  Reto Zach, the work done by a crow to break open a whelk (large marine snail) can be estimated by the function  W= (1+ 20 / H – 0.93) H,

 

Where H is the height (in meters) of the whelk when it is dropped. Source: Mathematics Teacher.

 

 

a. Find dW | dH

 

b. One can show that the amount of work is minimized when

dW | dH = 0.  Find the value of H that minimizes W.

 

c. Interestingly, Zach observed the crows dropping the whelks from an average height of 5.23 m. What does this imply?

 

 

 

 

 

 

 

 

 

Q8.(64-4.3) 64. Drug Reaction The strength of a person’s reaction to a certain drug is given by

 

R (Q) = Q (C – Q/3) 1/2.

 

where Q represents the quantity of the drug given to the patient and C is a constant.

 

a. The derivative R’( Q )is called the sensitivity to the drug.

Find  R’(Q).

 

b. Find the sensitivity to the drug if C = 59 and a patient is given 87 units of the drug.

 

c. Is the patient’s sensitivity to the drug increasing or decreasing where Q = 87?

 

 

Q9.(60-4.4) 60.Heat Index The heat index is a measure of how hot it really feels under different combinations of temperature and humidity. The heat index, in degrees Fahrenheit, can be approximated by

H(T) =T – 0.9971e 0.02086T { 1 – e0.0445(D -57.2)},

 

where the temperature T and dewpoint D are both expressed in degrees Fahrenheit. Source: American Meteorological Society.

 

a. Assume the dewpoint is D = 85 F. Find the function H(T).

 

b. Using the function you found in part a, find the heat index when the temperature T is 80 F.

 

c. Find the rate of change of the heat index when T = 80 F.

 

 

 

 

 

 

 

 

 

Q10.(68-4.5) 68. Street Crossing Consider a child waiting at a street corner for a gap in traffic that is large enough so that he can safely cross the street. A mathematical model for traffic shows that if the expected waiting time for the child is to be at most 1 minute, then the maximum traffic flow, in cars per hour, is given by

 

f (x ) =  29,000(2.322 – log x)/ x ,

 

Where x is the width of the street in feet. Find the maximum traffic flow and the rate of change of the maximum traffic flow with respect to street width for the following values of the street width. Source: An Introduction to Mathematical Modeling.

 

 

A. 30 ft                                 B. 40 ft

Statistics

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PROBLEM 1
Kathleen Vohs of the University of Minnesota and her coworkers carried out several randomized comparative experiments on the effects of thinking about money. Here’s part of one such experiment. Ask student subject to unscramble 30 sets of five words to make a meaningful phrase from four of the five words. The control group unscrambled phrases like “cold it desk outside is” into “it is cold outside.” The treatment group unscrambled phrases that lead to thinking about money, turning “high salary desk paying” into “a high-paying salary.” Then each subject worked a hard puzzle, knowing that they could ask for help. Here are the times in seconds until subjects asked for help:

 

Treatment group:
609 444 242 198 174 55 251 466 443
531 135 241 476 482 362 69 160

 

Control group:
118 272 412 290 140 104 55 189 126
400 91 63 87 142 141 373 156

 

The researcher suspected that money is connected with self-sufficiency, so that the treatment group would ask for help less quickly on the average. Do the data support this idea? Use a 5% level of significance.

 

EXPECTATIONS
– Draw graphs and charts when appropriate and necessary to demonstrate your reasoning! Label all graphs and charts!
– Display formulas. Write complete sentences to summarize your conclusions.
– If use any table values, clearly state which tables you used (e.g. Table A-2, etc.).
-Attach excel output when appropriate or necessary (e.g. a scatterplot, etc.)

HYPOTHESIS TESTING QUESTIONS
Your work for all statistical hypothesis testing questions should include the following:
1. Established Ho and Ha.
2. Summary statistics (either computed or given in the problem)
3. The name of the test (e.g. 2sampleTtest or T-test about correlation, etc.)
4. A formula to compute a test statistic (e.g. 1Prop-Z test statistic, etc.)
5. A p-value of the test and/or a critical value from a statistical table.
6. Clearly state the decision rule you use the reach a conclusion. (You may have to sketch a graph to show rejection regions.) Do you “Reject Ho” or do you “Fail to Reject Ho”?
7. State your conclusion in plain language. Use complete sentences.

 

We frequently hear the following terms used by businesspersons. What does each mean in economic terminology? A. spreading the overhead.

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Chapter 9
#6. We frequently hear the following terms used by businesspersons. What does each mean in
economic terminology?
A. spreading the overhead.
B. A break-even level of production
C. The efficiency of mass production.
#2. Dimex Fabrications Co., a small manufacturer of sheet-metal body parts for a major U.S.
automaker, estimates its long-run production function to be
Q= -0.015625K3L3 + 10 K2 L2
where Q is the number of body parts produced daily, K is the number of sheet-, metal presses in
its manufacturing plant, and L is the number of labor-hours per day of sheet-metal workers
employed by Dimex. Dimex is currently operating with eight sheet-metal presses.
a. What is the total product function for Dimex? The average product function? The marginal
product function?
b. Managers at Dimex can expect the marginal product of additional workers to fall beyond what
level of labor employment?
c. Dimex plan to employ 50 workers. Calculate total product, average product, and marginal
product
#3. The chief economist for Argus Corporation, a large appliance manufacturer, estimated the
firm’s short-run cost function for vacuum cleaners using an average variable cost function of the
form
AVC = a + bQ + cQ2
where AVC dollars per vacuum cleaner and Q number of vacuum cleaners produced each month. Total
fixed cost each month is $180,000. The following results were obtained:
DEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON F
OBSERVATIONS: 190 0.7360
39.428
0.001
VARIABLE

INTERCEPT
Q
Q2

PARAMETER
Estimate
194.93
-0.0305
0.0000024

STANDARD T-RATIO P-VALUE
Error
54.65
0.00789
0.00000098

.512
23.866
2.449

0.0029
0.0014
0.0262

a. Are the parameter estimates a, b, and c statistically significant at the 2 percent level of significance?
b. Do the results indicate that the average variable cost curve is U-shaped? How do you know?
c. If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average
variable cost? Marginal cost? Total variable cost? Total cost?
d. Answer part c, assuming that Argus produces 10,000 vacuum cleaners monthly.

e. At what level of output will average variable cost be at a minimum? What is minimum average variable
cost?

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 62 professional actors, it was found that 36 were extroverts. (a) Let p represent the proportion of all

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For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 62 professional actors, it was found that 36 were extroverts.
(a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to two decimal places.)
lower limit 
upper limit 

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5120 permanent dwellings on an entire reservation showed that 1683 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.)
lower limit 
upper limit 

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Santa Fe black-on-white is a type of pottery commonly found at archaeological excavations at a certain monument. At one excavation site a sample of 582 potsherds was found, of which 364 were identified as Santa Fe black-on-white.
(a) Let p represent the proportion of Santa Fe black-on-white potsherds at the excavation site. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 95% confidence interval for p. (Round your answers to three decimal places.)
lower limit 
upper limit 

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of 5994 physicians in Colorado showed that 3251 provided at least some charity care (i.e., treated poor people at no cost).
(a) Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit 
upper limit 

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

Case studies showed that out of 10,137 convicts who escaped from certain prisons, only 7582 were recaptured.
(a) Let p represent the proportion of all escaped convicts who will eventually be recaptured. Find a point estimate for p. (Round your answer to four decimal places.)

(b) Find a 99% confidence interval for p. (Round your answers to three decimal places.)
lower limit 
upper limit 

QSO510 Module 10

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QSO 510: Module 10

Notes: Before doing this assignment, do the practice problem posted under Apply and Discover. Word-process your answers within this document. Do not create a new file. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.

 

Problem

During the dinner hour, the distribution of the inter-arrival time of customers at a restaurant is estimated to be as shown below.  The mode of payment and the service times of the cash and credit card customers are shown in the following tables. Complete the tables and simulate the system for 20 customer arrivals and determine the average time a cash and credit card customer must wait in line before paying the cashier. Use Column A of the given random number table to determine the customer inter-arrival time, Column B to determine whether the customer pays with cash or credit, and Column C to determine the service time.

 

Inter-arrival time

Inter-arrival Time

Probability

Cumulative Probability

Random Number Interval

30 seconds

0.45

 

 

60 seconds

0.25

 

 

90 seconds

0.15

 

 

120 seconds

0.10

 

 

150 seconds

0.05

 

 

 

Mode of Payment

Payment Mode

Probability

Cumulative Probability

Random Number Interval

Cash

0.6

 

 

Credit Card

0.4

 

 

 

Cash Service Time

Service Time

Probability

Cumulative Probability

Random Number Interval

20 seconds

0.35

 

 

40 seconds

0.30

 

 

60 seconds

0.25

 

 

80 seconds

0.10

 

 


 

 

 

Credit Card Service Time

Service Time

Probability

Cumulative Probability

Random Number Interval

30 seconds

0.20

 

 

60 seconds

0.45

 

 

90 seconds

0.25

 

 

120 seconds

0.10

 

 

 

 

Random Numbers

(A)

(B)

(C)

6320

1094

1995

4630

7371

7971

8657

2809

3554

0030

5148

6300

5624

9115

5495

6728

1469

5165

5925

6480

9339

2829

2447

6997

7939

7031

1443

6476

8442

3574

3319

7387

0150

8134

1788

0933

1712

4891

7082

6317

1149

5025

6605

8822

4081

2734

9451

4100

0432

2990

7190

3441

8314

6822

0726

7176

5053

6969

2766

8284


 Complete the table below to show the results of the simulation.

 

Customer

Random Number

Arrival Time

Random Number

Mode of Payment

Random Number

Service Time

Service Time

Waiting Time

 

 

 

 

 

 

 

Begins

Ends

Cash

Credit

1

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

4

 

 

 

 

 

 

 

 

 

 

5

 

 

 

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

 

7

 

 

 

 

 

 

 

 

 

 

8

 

 

 

 

 

 

 

 

 

 

9

 

 

 

 

 

 

 

 

 

 

10

 

 

 

 

 

 

 

 

 

 

11

 

 

 

 

 

 

 

 

 

 

12

 

 

 

 

 

 

 

 

 

 

13

 

 

 

 

 

 

 

 

 

 

14

 

 

 

 

 

 

 

 

 

 

15

 

 

 

 

 

 

 

 

 

 

16

 

 

 

 

 

 

 

 

 

 

17

 

 

 

 

 

 

 

 

 

 

18

 

 

 

 

 

 

 

 

 

 

19

 

 

 

 

 

 

 

 

 

 

20

 

 

 

 

 

 

 

 

 

 
                     

Average Waiting Time (Cash)=

 

Average Waiting Time (Credit)=

 
                       

 

BSTA300 WEEK 7 ASSIGNMENT 2 Probability

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ASSIGNMENT NAME: ASSIGNMENT 2 – Probability
COURSE: BSTA300
WEEK NUMBER: 7
CONTACT: Instructor via Blackboard Mail
DUE DATE: See Critical Path document
A. INSTUCTIONS

Using Word, please answer the questions below. When answering the questions be sure to show your work. A formula sheet has been attached to help with some of the special characters and formula in your answers.
BE SURE TO STATE QUESTION NUMBER AND LETTER. (e.g. Question 1 b)
At the bottom of this page you will find two attached files:
A formula sheet, Formula .doc, that has two purposes:
To give you any formula you may need.
To allow you copy formula and special characters from the Word document into your Word answer sheet.
A template sheet, template2.doc, that you can use to answer the questions.
Download the attached files:
Click Formula .doc in the Attachments: section below.
Click Save for Internet Explorer. Firefox will open the file in Word.
Save the file in a folder you have set aside for class work (e.g. “BSTA300”).
Repeat steps i – iii to download template2.doc.
B. QUESTIONS

Question 1: (7 marks)
Olympia Sports store wants to determine whether or not to concentrate its advertising on athletic shoes for the “serious” athlete or the “weekend” athlete. The store also wants to know which type of use is the most popular. The marketing department gathered the following information from randomly selected customers.

Athlete Tennis Running Basketball
Serious 36 27 52
Weekend 54 66 30

Find the probability that if one customer is randomly selected he/she is a serious athlete and buys a shoe primarily for running.
Find the probability that if one customer is randomly chosen he/she is a serious athlete or an athlete who buys shoes for tennis.
Given that a customer buys shoes for basketball, find the probability that the customer is a weekend athlete.
If two customers are randomly chosen (without replacement), find the probability that they will both buy shoes primarily for tennis.

Question 2: (7 marks)
A couple plans to have 4 children.

List the different outcomes according to the gender of each child. Assume that these outcomes are equally likely.
How many events are possible?
Find the probability of getting exactly 2 girls.
Find the probability of getting exactly 2 children of each gender.

Question 3: (4 marks)

In a casino game craps, you can bet the next roll of the two dice with result in a total of 2. The probability of rolling 2 is 1/36. Find the odds against rolling 2.
If you bet $5 that the next roll of the dice will be 2, you will collect $155 (including your $5 bet) if you win. First identify the net profit, then find the payoff odds.

Question 4: (2 marks)
A supervisor must visit 8 different distribution locations around the country. She can visit them in any order, but wishes to find the most convenient sequence. How many sequences are possible?

Question 5: (4 marks)
There are 12 members on the board of directors for Cliffside General Hospital.

If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?
If they must form an ethics subcommittee of 4 members, how many different subcommittee are possible?

Question 6: (6 marks)
In a market study for Zellers, a researcher found that 70% of customers are repeat customers. If 12 customers are selected at random, find the probability of getting.

Exactly 9 of them are repeat customers
At least 9 of them are repeat customers
At most 9 of them are repeat customers