One method for estimating the availability of office space in large cities is to conduct a random sample of offices, and calculate the proportion of offices currently being used. Suppose that real estate agents believe that π = 0.70 of all offices are currently occupied, and decide to take a sample to assess their belief. They are considering a sample size of n = 40.
a) Show that this sample size is large enough to justify using the normal approximation to the sampling distribution of p.
b) What is the mean of the sampling distribution of p if the real estate agents are correct? c) What is the standard deviation of the sampling distribution of p if the real estate agents are correct?
d) If the real estate agents are correct, what is the probability that a sample proportion, p, would differ from π = 0.70 by as much as 0.05?
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