A landlord is considering raising the monthly rent because of increased costs. He is concerned about competition, and will only increase the rent if the current local city vacancy rate is below $20 \%$. Suppose the owner has decided to take a simple random sample of apartments in the city and estimate the vacancy rate. He is considering a sample 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 $b$ approximately 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 less than $0.20$ even though the population proportion is $0.30$ ?

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The Answer of A landlord is considering raising the monthly rent because of increased costs. He is concerned about competition, and will only increase the rent if the current local city vacancy rate is below $20 \%$. Suppose the owner has decided to take a simple random sample of apartments in the city and estimate the vacancy rate. He is considering a sample 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 $b$ approximately 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 less than $0.20$ even though the population proportion is $0.30$ ?

A Landlord Is Considering Raising the Monthly Rent Because of Increased