Assume that the standard deviation of monthly rents paid by students in a particular town is $40. A random sample of 100 students was taken to estimate the mean monthly rent paid by the whole student population.
a. What is the standard error of the sample mean monthly rent?
b. What is the probability that the sample mean exceeds the population mean by more than $5? (Hint: Look at the z formula. What is the result of the numerator of the formula?)
c. What is the probability that the sample mean is more than $4 below the population mean?
d. What is the probability that the sample mean differs from the population mean by more than $3?