High-rent district: The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2693. Assume the standard deviation is $517 A real estate firm samples 115 apartments. Use the TI-84 Plus calculator.

a) What is the probability that the sample mean rent is between $2562 and $2662? Round the answer to at least four decimal places.

b) Find the 65th percentile of the sample mean. Round the answer to at least two decimal places.

c) Would it be unusual if the sample mean were greater than $2751? Round answer to at least four decimal places.

d) Do you think it would be unusual for an individual to have a rent greater than $2751? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.