Waiting times at banks tend to follow a distribution which is skewed to the right. Suppose the mean waiting time at a particular bank is 3 minutes with a standard deviation of 2.

a. Do you have enough information to find the probability a single customer waits between 2.5 and 3.5 minutes?

No, because this distribution is not normally distributed.Yes, because of the central limit theorem we can use normal approximation to find this probability.

b. Do you have enough information to find the probability that the mean waiting time of60customers is between 2.5 and 3.5 minutes?

No, because this distribution is not normally distributed.Yes, because of the central limit theorem we can use normal approximation to find this probability.

c. Find probability for part b.

d. Why can we find the probability for part b, but not part a ?

I have no earthly clue.Because if the population distribution is not normal there must be a sufficiently large enough sample to be able to assume the distribution of the SAMPLE MEAN is normal.