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A personnel manager must review 16 employees every month. From past experience, she knows that individual reviews take an average of 4 hours with a standard deviation of 1.2 hours. (a) Find the probability that the mean time for the interviews will be between 3.5 and 4.25 hours. (b) Find the 95th percentile of the mean time to complete the interview. ANSWER: (a) (b) Problem 2 (Chapter 7) A random variable has a mean of 80 and a standard deviation of 12. A sample size of 95 is randomly drawn from the population. (a) Find the probability that the sum of the 95 values is greater than 7650. (b) Find the probability that the sum of the 95 values is less than 7400. ANSWER: (a) (b) Problem 3 (Chapter 7) A manufacturer produces 25-pound lifting weights. The lower actual weight is 24 pound, and the highest weight is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken. (a) Find the probability that the mean actual weight for the 100 weights is greater than 25.2. (b) Find the 90" percentile for the mean weight of the 100 weights. Hint: Let X be the weight of one of the weights. Then X ~ Uniform(24,26). So the mean of X is 25 and the standard deviation for X is 0.5774 (See Excel Reference sheet on Blackboard.) ANSWER: (a) (b)