I would like to get answers to the 7 questions for this problem. Explanations can be brief, but please provide basic calculator commands used to reach the answer. This will serve as a guide for me to work the other problems in this chapter. Thanks, David.

It is reported that the mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2631 and the standard deviation is $500. A real estate firm randomly samples 100 apartments to study. Assume the distribution of monthly rents for a one-bedroom apartment without a doorman is relatively normal.

Is the sampling distribution normal? Why? What is the mean and what is the standard deviation of this sampling distribution.What is the probability that a randomly selected Manhattan apartment has a rent more than $2700?What is the probability that a sample mean rent is more than $2700?What is the probability that a sample mean rent is between $2500 and $2600?Find the 60^th percentile of the sampling distribution of sample mean.Would it be unusual if the sample mean were greater than $2800? Explain.Would it be unusual for an individual apartment to have a rent more than $2800? Explain