50. Let have the standard normal distribution. a. Find ( < 2.51 or > 1.76). b. Find ( < 1.76 or > 2.51). 51. The heights of women are normally distributed. Suppose it is known that the population standard deviation is 2.5 inches. a. Alice, a 63 inch tall woman, has a standard score of -0.32 for this distribution. Use this information to find the population mean. b. If Bianca is 65 inches tall, compute the standard score for her height. 52. Suppose that the age a child gets their first cell phone follows a normal distribution with a mean of 10.0 years, and a standard deviation of 1.5 years. a. What is the 72nd percentile for this distribution? b. Approximately what percentage of children gets their first cell phone at an age between 8.5 and 11.5 years? 53. Suppose that during the month of February, the low temperature in Detroit follows a normal distribution with a mean of 27 and a standard deviation of 5. For a randomly selected day in February, what is the probability that the low temperature on that day differs from the population mean by more than 7? 54. Suppose the scores on the SAT math test are normally distributed with a mean of 508 and standard deviation of 100. What score would a student need to be in the top 5% of all students