Question

Suppose the waiting time at a certain checkout counter is bimodal. With probability 0.95, the waiting time follows an exponential distribution with a mean waiting time of five minutes. With probability 0.05, the waiting time equals 30 minutes.

a) Compute the mean waiting time at the checkout counter.

b) Compute the variance of the waiting time at the checkout counter.

c) Compute the probability that an individual customer waits longer than 5 1/2 minutes at the checkout counter.

d) Using the statistical software R, sample n individuals from the bimodal distribution described above. For N=10,000 iterations, compute the average waiting time for n=5, n=15, n=50, n=100 individuals and plot a histogram of the sampling distribution for the mean waiting time.

e) How large a sample do you need for the sampling distribution of the mean waiting time to approximate a normal distribution?

Answer 1