# Suppose the grading for a course project can only have 6 possible outcomes

Suppose the grading for a course project can only have 6 possible outcomes; 100, 90, 80, 70, 60, 50, and 0. Let the random variable X be the scores on the project. Suppose X has the following distribution:

X |
P(X=x) |

100 |
0.1 |

90 |
0.25 |

80 |
0.3 |

70 |
0.15 |

60 |
0.1 |

50 |
0.09 |

0 |
0.01 |

a. What is the probability that X is AT MOST 70?

b. What is the probability that X is AT LEAST 80%?

c. What is the probability that X is MORE than 80?

d. What is the probability that X is LESS than 70?

e. Compute the expected value for this random variable (see page 269 of text).