Question

Suppose the waiting time, in minutes, at a checkout line in a local super market follows a Uniform distribution in the interval (1,6)

a. How long is a randomly chosen customer at the super market expected to wait at the checkout counter?

b. What is the probability that a randomly chosen customer at the super market will wait between 2 and 5 minutes to be checked out?

c. Suppose a random sample of 100 customers is taken at the super market. What is the probability that their average waiting time at the checkout counter is between 2 and 5 minutes?

d. Compare your answers to parts b and c. Why are they different?

e. if X=waiting time, in minutes, at a checkout line, then X~_( _ , _ )

f. if X=average waiting time, in minutes, at a checkout line for random samples of n customers, then X~_ ( _ , _ ) for N>=30

g. Suppose a random sample of 200 customers is taken at the super market, what is the probability that their total waiting time at the checkout counter excesses 700 minutes?

h. if Ex=total waiting time, in minutes, at a checkout line for random samples of n customers, then Ex ~ _ ( _ , _ ) for n>=30

Answer 1

d) The difference is because that we have done uniform to normal approximation for a random sample for 100 customers but the earlier probability was of a single customer who follows a uniform distribution