Scores on a standardized exam for emotional intelligence in middle schoolers are normally distributed with a mean of 142 and a population standard deviation of 21.Find:
(a) the probability that a single test score selected at random will be greater than 150:
(b) the probability that a random sample of 10 scores will have a mean greater than 149.
(c) the probability that a random sample of 49 scores will have a mean greater than 149:
(d) the probability that the mean of a sample of 27 scores will be either less than 139 or greater than 149.