# Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A).

**SECOND EXAM**

# Econ 205 Name————————————

**Last FIRST**

**(1 point)**

1. Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.

a. What is the probability that you will receive a Merit scholarship? (1 point)

b. Are events A and M mutually exclusive? Why or why not? Explain, using probabilities. (1 point)

c. What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? (1 point)

d. Are the two events, A and M, independent? Explain, using probabilities.

(1 point)

2. The probability distribution for the number of goals the Pandas soccer team makes per game is given below.

Number of Goals | Probability |

0 | 0.05 |

1 | 0.15 |

2 | 0.35 |

3 | 0.30 |

4 | 0.15 |

a. What is the expected value of number of goals per game? (1point)

b. What is the probability that in a given game the Pandas will score at least 1 goal? (1point)

c. What is the probability that in a given game the Pandas will score more than 4 goals? (1 point)

3. The assembly time for a product is uniformly distributed between 6 and 10 minutes.

a. What is the probability of assembling the product in exactly 6 minutes? (1 point)

b. Compute the probability of assembling the product within an interval of 6 to 12 minutes. (1 point)

c. Compute the probability of assembly time of no longer than 8 minutes. (1 point)

4. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

a. What is the probability of a player weighing at least 241.25 pounds? (2 points)

b. 97.5% of players will weigh at least how many pounds? (2 points)

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