A Landlord Is Considering Raising the Monthly Rent Because of Increased

Essay

A landlord is considering raising the monthly rent because of increased costs. He isconcerned about competition, and will only increase the rent if the current local cityvacancy rate is below 20%. Suppose the owner has decided to take a simple randomsample of apartments in the city and estimate the vacancy rate. He is considering asample size of n = 40. Suppose further that the actual vacancy rate is 0.30.
a) Show that this sample size is large enough for the sampling distribution of $\hat{p}$ to bapproximately normal.
b) What is the mean of the sampling distribution of $\hat{p}$ ?
c) What is the standard deviation of the sampling distribution of $\hat{p}$ ?
d) What is the approximate probability that a sample proportion, $\hat{p}$ , would be lessthan 0.20 even though the population proportion is 0.30?