By statistics, faculty with rank of assistant professor (AP) finishing their 2nd year of employment at a higher education institution in Ontario earn an average of $ 75,360 per year with a standard deviation of $2,800. In an attempt to verify this salary level, a random sample of 40 AP with 2 years of experiment was selected from a personnel database for all higher education institutions in Ontario.
a. Describe the sampling distribution of the sample mean X of the average of these 40 AP.
b. Within what limit would you expect the sample mean to fall with probability .95?
c. If the random sample actually produced a sample mean X = 72, 000, would you consider this rather unusual? What conclusion might you draw then?