Candidates for promotion at a city police department are required to take a written aptitude test. scores on this test are normally distributed with a mean of 230 and a standard deviation of 50. a random sample of 9 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 210? (c)what is the probability that the sample mean score is more than 245? (d)suppose that the population standard deviation is, in fact, 30, rather than 50. without doing the calculations, state how this would change your answers to parts (a), (b), and (c). illustrate your conclusions with the appropriate graphs.