A certain university claims its recent graduates earn an average () annual income of $60,000.

A certain university claims its recent graduates earn an average (μ) annual income of $60,000. We have a reason to question the legitimacy of this claim and decide to test it out on a random sample of 100 alumni. In the process, we get a sample mean (X̅) of only $57,500. Suppose we know hypothetically that the standard error of the sample mean (σx̅) is $1,000. How probable (P) is it that we would get a sample mean of $57,500 or less if the true population mean is actually $60,000? Do you think the university told the truth?