Q 1. ACME Fruit Distributing knows that for the last four years, the mean ( or average ) time it takes a particular truck to make its round has been 6.32 hours with standard deviation 0.41 hours.

(a) Suppose you plan to observe this truck 40 times. What is the approximate distribution of the random sample mean time? Also specify its parameters.

(b) What is the approximate probability that this random sample mean (with n = 40) will be more than 6.7 hours?

(c) The truck route driver recently retired and Kyle took his place. Would observing Kyle's time on one particular day to be 6.1 hours cause you to think he is certainly a better driver than the previous one? Explain.

(d) Would observing Kyle's mean (average) time on 40 consecutive days to be 6.1 hours cause you to think he is certainly a better driver than the previous one? Explain.

Q 2. Sixty two percent of 12th graders attend school in a particular urban school district. If a sample of 500 12th grade children is selected, find the exact probability that at least 290 are actually enrolled. Use normal approximation to compute the probability.