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 60th 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.