1. (8 points) If the IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
(a) (3 pts) Find the probability that a randomly selected person has an IQ score between 88 and 112. (Show work)
(b) (2 pts) If 100 people are randomly selected, what is the standard deviation of the sample mean IQ score. (Show work)
(c) (3 pts) If 100 people are randomly selected, find the probability that their mean IQ
score is greater than 103. (Show work)
2. (8 points) Imagine you are in a game show. There are 4 prizes hidden on a game board with 16 spaces. One prize is worth $4000, another is worth $1500, and two are worth $1000. You have to pay $50 to the host if your choice is not correct.
(a) (6 pts) What is your expected winning in this game? (Show work)
(b) (2 pts) If you are offered a sure prize of $400 in cash, and you can just take the money without playing the game. What would be your choice? Take the money and run, or play the game? Please explain your decision.
3. (7 points) Mimi just started her tennis class three weeks ago. On average, she is able to return 15% of her opponent’s serves. If her opponent serves 10 times, please answer the following questions:
(a) (5 pts) What is the probability that she returns at most 2 of the 10 serves from her opponent? (Show work)
(b)(2 pts) How many serves can she expect to return? (Hint : What is the expected value?) (Show work)
4. (4 points) Men’s heights are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. Mimi is designing a plane with a height that allows 95% of the men to stand straight without bending in the plane. What is the minimum height of the plane? (Show work)
5. (6 points) There are 7 seniors and 3 juniors in the statistics club, and a team of 5 will be randomly selected to attend the Joint Statistical Meetings in Montréal.
(b) What is the probability that none of the juniors are picked in this team of 5? (Show work)
(c) What is the probability that 2 of the juniors are picked in this team of 5? (Show work)
6. (4 points) There is a 1% delinquency rate for consumers with credit rating scores above 800. If UMUC Credit Union provides large loans to 10 people with credit rating scores above 800, what is the probability that at least one of them become delinquent? (Show work)