Question

Suppose that college faculty with the rank of professor at two year institutions earn an average of $52,500 per year with a standard deviation of $4,000. in an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all two-year instituations in the united states
C) calculate the probability the sample mean x-bar is greater than $55,000.

D) If you drew a random sample with the mean $55,000 would you consider this sample unusual? What conclusions might you draw?

Answer 1

Let x be a random variable representing the mean saraly of professors at two year institutions, then
P(x > 55000) = 1 - P(z < (55000 - 52500)/4000) = 1 - P(z < 0.625) = 1 - 0.73401 = 0.26599