820 CHAPTER 12 Statistics Automobile Speed In Exercises 67–72, assume that the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 62 mph and a standard deviation of 5 mph. 67. What percent of cars are traveling faster than 62 mph? 50% 68. What percent of cars are traveling between 58 mph and 66mph? 57.62% 69. What percent of cars are traveling slower than 56 mph? 11.51% 70. What percent of cars are traveling faster than 70 mph? 5.48% 71. If 200 cars are selected at random, how many will be traveling slower than 56 mph? ≈ 23 cars 72. If 200 cars are selected at random, how many will be traveling faster than 70 mph? ≈ 11 cars In Exercises 73–76, assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. 73. Determine the percent of females with a pulse rate between 70 beats per minute and 78 beats per minute. 25.1% 74. Determine the percent of females with a pulse rate greater than 88 beats per minute. 13.14% 75. In a random sample of 500 females, how many will have a pulse rate less than 70 beats per minute? ≈ 187 females 76. In a random sample of 500 females, how many will have a pulse rate greater than 88 beats per minute? ≈ 66 females Cost of Day Care In Exercises 77–82, assume the annual day-care cost per child is normally distributed with a mean of $12 000 , and a standard deviation of $2000. 77. What percent of day-care costs are more than $13,200 per child annually? 27.43% 78. What percent of day-care costs are between $10,000 and $13,000 per child annually? 53.28% 79. What percent of day-care costs are more than $17,000 per child annually? 0.62% 80. What percent of day-care costs are less than $17,000 per child annually? 99.38% 81. In a random sample of 120 families that use day care, how many pay more than $11,000 annually per child? ≈ 83 families 82. In a random sample of 120 families that use day care, how many pay between $10,000 and $13,000 annually per child? ≈ 64 families 83. Fitness Fit for Life gym guarantees that new members will bench press at least 20 additional pounds of weight in their first month of membership or their registration fee will be refunded. If the amount of additional weight members bench press in their first month is normally distributed with a mean of 24.5 pounds and a standard deviation of 3.24 pounds, determine the percent of customers who will be able to claim a refund. 8.23% 84. Battery Warranty The warranty on a car battery is 36 months. If the breakdown times of this battery are normally distributed with a mean of 46 months and a standard deviation of 8 months, determine the percent of batteries that can be expected to require repair or replacement under warranty. 10.56% 85. Coffee Machine A vending machine that dispenses coffee does not appear to be working correctly. The machine rarely gives the proper amount of coffee. Some of the time the cup is underfilled, and some of the time the cup overflows. Does this variation indicate that the mean number of ounces dispensed has to be adjusted, or does it indicate that the standard deviation of the amount of coffee dispensed by the machine is too large? The standard deviation is too large. 86. Grading on a Normal Curve Mr. Sanderson marks his class on a normal curve. Those with z-scores with ≥ z 1.80 will receive an A, those with ≤ < z 1.10 1.80 will receive a B, those with − ≤ < z 1.20 1.10 will receive a C, those with − ≤ < − z 1.90 1.20 will receive a D, those with < − z 1.90 will receive an F. Determine the percent of grades that will be an A, B, C, D, and F. A: 3.59%, B: 9.98%, C: 74.92%, D: 8.64%, F: 2.87% 87. Consider the following normal curve, representing a normal distribution, with points A B, , and C. One of these points corresponds to the mean, one point corresponds to the mean plus one standard deviation, and one point corresponds to the mean minus two standard deviations. A B C a) Which point corresponds to the mean? B b) Which point corresponds to the mean plus one standard deviation? C c) Which point corresponds to the mean minus two standard deviations? A Vasin Leenanuruksa/123RF $ $ $ $ $ $ Jules Selmes/Pearson Education Ltd
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