The Real Estate Group NY reports that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2631. Assume the standard deviation is $500. A real estate firm samples 100 apartments.

a. What is the probability that the sample mean rent is greater than $2700?

b. What is the probability that the sample mean rent is between

$2500 and $2600?

c. Find the 60th percentile of the sample mean.

d. Can you tell whether it would be unusual if the sample mean were greater than $2800?

e. Do you think it would be unusual for an individual apartment to have a rent greater than $2800? Explain.