# slide 2

53. An airline knows from experience that the distribution of the number of suitcases that get lost each
week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability
that during a given week the airline will lose less than 20 suitcases? A: 0.8944

54. An airline knows from experience that the distribution of the number of suitcases that get lost each
week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability
that during a given week the airline will lose more than 20 suitcases? A: 0.1056

55. An airline knows from experience that the distribution of the number of suitcases that get lost each
week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability
that during a given week the airline will lose between 10 and 20 suitcases? A: 0.8314

56. Assume that the salaries of elementary school teachers in the United States are normally
distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at
random, find the probability that he or she makes more than $36,000. A: 0.0918

57. Assume that the salaries of elementary school teachers in the United States are normally
distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at
random, find the probability that he or she makes less than $28,000. A: 0.0918

58. Assume that the heights of women are normally distributed with a mean of 63.6 inches and a
standard deviation of 2.5 inches. The cheerleaders for a local professional basketball team must be
between 65.5 and 68.0 inches. If a woman is randomly selected, what is the probability that her
height is between 65.5 and 68.0 inches? A: 0.1844

59. The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a
standard deviation of 15 days. A baby is premature if it is born three weeks early. What percent of
babies are born prematurely? A: 8.08%

60. The distribution of cholesterol levels in teenage boys is approximately normal with μ = 170 and
σ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention.
What percent of teenage boys have levels between 170 and 225? A: 3.36%

61. Assume that blood pressure readings are normally distributed with μ = 120 and σ = 8. A blood
pressure reading of 145 or more may require medical attention. What percent of people have a
blood pressure reading greater than 145? A: 0.09%

62. Assume that the heights of American men are normally distributed with a mean of 69.0 inches and
a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between
64 and 78 inches. Find the percent of men meeting these height requirements. A: 96.26%

73. Find the z-scores for which 90% of the distributionʹs area lies between -z and z A: (-1.645, 1.645)

74. Find the z-scores for which 98% of the distributionʹs area lies between -z and z. A: (-2.33, 2.33)

75. Find the z-score for which 70% of the distributionʹs area lies to its right A: -0.53

76. Find the z-score that is greater than the mean and for which 70% of the distributionʹs area lies to
its left. 0.53

77. Use a standard normal table to find the z-score that corresponds to the cumulative area of 0.7019. A: 0.53

78. Find the z-score that has 93.82% of the distributionʹs area to its right. A: -1.54

79. Find the z-score for which 99% of the distributionʹs area lies between -z and z. A: (-2.575, 2.575)

80. IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the
x-score that corresponds to a z-score of 2.33. A: 134.95

81. IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the
x-score that corresponds to a z-score of -1.645. A: 75.3

82. The scores on a mathematics exam have a mean of 77 and a standard deviation of 8. Find the
x-value that corresponds to the z-score 2.575. A: 97.6 84. ) Compare the scores: a score of 75 on a test with a mean of 65 and a standard deviation of 8 and a
score of 75 on a test with a mean of 70 and a standard deviation of 4. A: The two scores are statistically the same

85. Compare the scores: a score of 88 on a test with a mean of 79 and a score of 78 on a test with a
mean of 70. A. you cannot determine.

86. Compare the scores: a score of 220 on a test with a mean of 200 and a standard deviation of 21 and
a score of 90 on a test with a mean of 80 and a standard deviation of 8. A: A score of 90 with a mean of 80 and a standard deviation of 8 is better.

87. Two high school students took equivalent language tests, one in German and one in French. The
student taking the German test, for which the mean was 66 and the standard deviation was 8,
scored an 82, while the student taking the French test, for which the mean was 27 and the standard
deviation was 5, scored a 35. Compare the scores A: A score of 82 with a mean of 66 and a standard deviation of 8 is better

88. SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8
and a standard deviation of 4.8. A student takes both tests while a junior and scores 1130 on the
SAT and 25 on the ACT. Compare the scores. A: A score of 25 on the ACT test was better.

89. SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8
and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the
SAT and 16 on the ACT. Compare the scores. A: A score of 860 on the SAT test was better.

92. Assume that the salaries of elementary school teachers in the United States are normally
distributed with a mean of $28,000 and a standard deviation of $3000. What is the cutoff salary for
teachers in the bottom 10%? A: $24,160