Homework 6 Solutions.pdf

1 Stat 133 Autumn 2007 NAME__________________ Homework #6 (10 points) GROUP #_______________ Due Thursday Nov 8 (beginning of recitation) 1. Which of the following is a NOT a discrete random variable? a. The time between accidents on a busy highway. b. The number of accidents on a busy highway. c. The number of red cars that go by, in a random sample of 100. d. All of the above are discrete random variables. 2. Assume X and Y are ANY two random variables (not necessarily independent!) Answer True or False for each one below: a. ? (X+Y) = ? (X) + ? (Y) TRUE FALSE b. ?(X+Y) = ? (X) + ? (Y) TRUE FALSE c. ? (4X+5Y) = 4?? (X) + 5 ? (Y) TRUE FALSE 3. Suppose ??(X,Y) =0. Then X and Y must be independent. a. True b. False 4. What proportion of the data from a normal distribution lie within two standard deviations on either side of the mean (using the table)? a. 0.3413 b. 0.4772 c. 0.6826 d. 0.9544 5. If your value of Z is Z = .80 then you are at the 80th percentile of the Z distribution. a. True b. False Use the following information for problems 6-8: Suppose approximately 80% of OSU students are in favor of the smoking ban. Two OSU students are selected at random. 6. What is the probability that both of them support the smoking ban? P(Both support) = (0.8)(0.8) = 0.64 ANS_______ 7. What is the probability that both of them oppose the smoking ban? P(Both Oppose) = P(Neither Supports) = (1 - 0.8)(1 - 0.8) = 0.04 ANS_______ 8. What is the probability that at least one of them supports the smoking ban? P(At Least 1) = 1 ? P(Both Oppose) ? P(Both Support) = 1 ? 0.68 = 0.32 ANS_______ 0.64 0.04 0.32 2 Use the following information for problems 9-10: Let X be the amount of cash a customer withdraws from their account at the bank. Let X have a Normal distribution with mean $100 and standard deviation $25. 9. Find the 75th percentile for X. 75th Percentile ? Z = 0.67 ? 2510067.0 ?? X ? X = $116.75 (z-table) ANS_________ 10. Find the probability that one customer chosen at random withdraws less than $60. 60.12510060 ?????? ? ?XZ P(X < 60) = P(Z < -1.60) = 0.0548 (z-table) ANS__________ $116.75 0.0548 rumsey Stat 133