Candidates for employment at a city fire department are required to take a written aptitude test. Scores on this test are normally distributed with a mean of 280 and a standard deviation of 60. A random sample of nine test scores was taken.
a. What is the standard error of the sample mean score?
b. What is the probability that the sample mean score is less than 270?
c. What is the probability that the sample mean score is more than 250?
d. Suppose that the population standard deviation is, in fact, 40, rather than 60. Without doing the calculations, state how this would change your answers to parts (a), (b), and (c). Illustrate your conclusions with the appropriate graphs.