The 2006 AAPA survey of the population of physicians’ assistants who were working full time reported a mean annual income of $84,396 and standard deviation of $21,975. (Source: Data from 2006 AAPA survey [www.aapa.org].)
a. Suppose the AAPA had randomly sampled 100 physicians’ assistants instead of collecting data for all of them. Describe the mean, standard deviation, and shape of the sampling distribution of the sample mean.
b. Using this sampling distribution, find the z -score for a sample mean of $80,000.
c. Using parts a and b, find the probability that the sample mean would fall within approximately $4000 of the population mean.