1. (8 points) If the IQ scores are normally distributed with a mean of 100 and a standard
deviation of 15.
(a) Find the probability that a randomly selected person has an IQ score between 88 and 112.
(Show work)
(b) 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) What is your expected winning in this game? (Show work)
(b) 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
25% of her opponent
Solution
Well there are ways to calculate these. Or you can use some common sense. 15.
With a mean of 100 for a normal distribution, there is 50% chance for <100. So for <115, there'd
be an even larger chance. Only one answer has a % larger than 50%. So B. 16. Similar
reasoning. The probability has to be less than 50%. So D. 17. This is likely to be fairly big.
Certainly NOT B. You might want to calculate z-scores for 88 and 112. z = (88 - 100) / 15 = -.8
z = (112 - 100) / 15 = .8 So, use a z-table to lookup the probability -.8 < z < .8. I know between -
1 and 1 is 68%.