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 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. (2 pts)

b) What is the mean of the sampling distribution of p if the real estate agents are correct? (2pts)

c) What is the standard deviation of the sampling distribution of p if the real estate agents are correct? (4 pts)

d) If the real estate agents are correct, what is the probability that a sample proportion, p, would differ from by as much as 0.05? (8 pts)

2 answers

a)
b)1
c)standard deviation=

c) 0.07246