3. suppose college faculty members 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 institutions in the united states. a. what are the mean and standard deviation of the sampling distribution for n = 60? (2 points) b. what's the shape of the sampling distribution for n = 60? (1 point) c. calculate the probability the sample mean x-bar is greater than $55,000. (1 point) d. if you drew a random sample with a mean of $55,000, would you consider this sample unusual? what conclusions might you draw? (1 point)