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Presentation RubricContent and Organization 70 pointsPoints Po.docx

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1. (8 points total) Suppose that A, B, and C are events. For each of the following statements, circle the T if it is true and the F if it is false. If it is true, briefly explain your reasoning (2-3 sentences) in the space provided. If it is false, give an example for which the statement is false (also called a counterexample). (a) (4 points) If P(A)+P(B)+P(C) = 1, then the events A, B, and C are disjoint. T F (b) (4 points) For any two events A and B, P(AUB) = P(A)+P(B). T F Solution a) False; If Pr(A) = .5, Pr(B) = .3. Pr(C) = .2, where Pr(A?B)=.2 then Pr(A)+Pr(B)+Pr(C) will equal 1 but the events are not disjoint. The Pr(A?B?C) would be < 1. b) False; The Pr(AUB) would equal Pr(A) + Pr(B) if the events A and B are disjoint. If they are not, then the Pr(AUB) would equal Pr(A) + Pr(B) - Pr(A?B)..

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- 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%.

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