A year-old study found that the service time for all drive-thru customers at the Stardust Coffee Shop is uniformly distributed between 3 and 6 minutes. Assuming the service time distribution has not changed, a random sample of 49 customers is taken and the service time for each is recorded.
a. Calculate the mean and standard deviation of service times for all drive-thru customers at the Stardust Coffee Shop.
b. What is the probability that a sample of 49 customers would have a sample mean of 4.25 minutes or more if the true population mean and standard deviation for service times are as calculated in part a?
c. How can the probability in part b be determined when the population of service times is not normally distributed?