The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2,674. Assume the standard deviation is $508. A real estate firm samples 108 apartments.

a. What is the probability that the sample mean rent is greater than $2,744?

b. What is the probability that the sample mean rent is between $2,543 and $2,643?

c. Find the 80th percentile of the sample mean.

d. Would it be unusual if the sample mean were greater than $2,704?

e. Do you think it would be unusual for an individual to have a rent greater than $2,704? Explain. Assume the variable is normally distributed.