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14. Given thatx is normally distributed with a mean of 9.3 and a standard devia- 15. l6. 17. 18. 19. tion of 2.1, nd each of the following. a. The area under the curve between 8.0 and 10.0. b. The area under the curve between 10.0 and 14.5. c. The probability that a randomly selected value of x is between 5.0 and 8.0. d. The probability that a randomly selected value is greater than 7.5. e. The proportion of the population that is greater than 15.0. f. The proportion of the population that is less than 12.0. State three interpretations of the statement: \"P(10 134.5) when x is randomly selected from a normal population with a mean of 128.9 and a standard deviation of6.2. If the heights of 5,000 students are normally distributed with a mean of 68.5 inches and a standard deviation of3.2 inches, find each of the following. a. The proportion of students who are shorter than 62 inches. b. The probability that a person picked at random from the group is taller than 72 inches. 0. The number of students who are shorter than 62 inches. In a league of 100 bowlers, the bowling averages are normally distributed with a mean of 155.6 and a standard deviation of 7.9. a. What percentage of the bowlers in this league have an average below 150'? b. If a bowler is selected at random from this league, what is the probability that his average is between 150 and 170? c. How many of the bowlers have an average above 170'? If the birth weights of infants are normally distributed with a mean weight of 7 pounds 2.4 ounces ( 1 14.4 oz.) and a standard deviation of 1 pound 1.2 ounces (17.2 02.), find each of the following. a. The proportion of infants who weight more than 8 pounds. b. The proportion of infants who weigh less than 5 pounds. 0. The number of infants who can be expected to weigh between 7 pounds and 8 pounds in a list of 500 such infants