Suppose that college faculty with the rank of professor at public 2-year institutions earn an average of $75,878 per year† with a standard deviation of $4,000. In an attempt to verify this salary level, a random sample of 80 professors was selected from an appropriate database. (a) Describe the sampling distribution of the sample mean x. The sampling distribution is nonnormal with mean μ and standard deviation 4,000. The sampling distribution is nonnormal with mean μ and standard deviation 4,000/ 80 . The sampling distribution is normally distributed with mean μ and standard deviation 4,000/ 80 . The sampling distribution is normally distributed with mean μ and standard deviation 4,000. The sampling distribution is normally distributed with mean 80 and standard deviation 4,000. (b) Within what limits would you expect the sample average to lie, with probability 0.95? (Round your answers to two decimal places.) lower limit $ upper limit $ (c) Calculate the probability that the sample mean x is greater than $78,100. (Round your answer to four decimal places.) (d) If your random sample actually produced a sample mean of $78,100, would you consider this unusual? What conclusion might you draw? This sample mean is somewhat unlikely if the average salary is $75,878. This average salary may no longer be correct. This sample mean is not unlikely if the average salary is $75,878. There is no reason to doubt the reported average salary