308 Chapter 7 The Normal Distribution a. What proportion of women have blood pressures lower than 70? 0.1446 Tech: 0.1444 b. What proportion of women have blood pressures between 75 and 90? 0.5438 Tech: 0.5421 c. A diastolic blood pressure greater than 90 is classified as hypertension (high blood pressure). What proportion of women have hypertension? 0.1685 Tech: 0.1686 d. Is it unusual for a woman to have a blood pressure lower than 65? No 28. Baby weights: According to a recent National Health Statistics Reports, the weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. a. What proportion of babies weigh more than 13 pounds? b. What proportion of babies weigh less than 15 pounds? c. What proportion of babies weigh between 10 and 14 pounds? 0.5361 Tech: 0.5335 d. Is it unusual for a baby to weigh more than 17 pounds? Yes 29. Check your blood pressure: The Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.5 and standard deviation 9.9. a. Find the 30th percentile of the blood pressures. b. Find the 67th percentile of the blood pressures. 84.86 c. Find the third quartile of the blood pressures. 30. Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation 2.7 pounds. a. Find the 81st percentile of the baby weights. b. Find the 10th percentile of the baby weights. 8.04 c. Find the first quartile of the baby weights. 9.69 Tech: 9.68 31. Fish story: According to a report by the U.S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the Arolik River in Alaska is 481 millimeters with a standard deviation of 41 millimeters. Assume these lengths are normally distributed. a. What proportion of six-year-old rainbow trout are less than 450 millimeters long? 0.2236 Tech: 0.2248 b. What proportion of six-year-old rainbow trout are between 400 and 500 millimeters long? 0.6533 Tech: 0.6544 c. Is it unusual for a six-year-old rainbow trout to be less than 400 millimeters long? Yes 32. Big chickens: According to thepoultrysite.com, the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams. a. What proportion of broilers weigh between 1100 and 1200 grams? 0.0855 Tech: 0.0854 b. What is the probability that a randomly selected broiler weighs more than 1500 grams? 0.2420 Tech: 0.2414 c. Is it unusual for a broiler to weigh more than 1550 grams? No 33. Fish story: The U.S. Fish and Wildlife Service reported that the mean length of six-year-old rainbow trout in the Arolik River in Alaska is 481 millimeters with a standard deviation of 41 millimeters. Assume these lengths are normally distributed. a. Find the 58th percentile of the lengths. 489.20 Tech: 489.28 b. Find the 76th percentile of the lengths. 510.11 Tech: 509.96 c. Find the first quartile of the lengths. 453.53 Tech: 453.35 d. A size limit is to be put on trout that are caught. What should the size limit be so that 15% of six-year-old trout have lengths shorter than the limit? 438.36 Tech: 438.51 34. Big chickens: A report on thepoultrysite.com stated that the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams. a. Find the 22nd percentile of the weights. 1263.03 Tech: 1262.68 b. Find the 93rd percentile of the weights. 1625.28 Tech: 1624.60 c. Find the first quartile of the weights. 1279.13 Tech: 1278.41 d. A chicken farmer wants to provide a money-back guarantee that his broilers will weigh at least a certain amount. What weight should he guarantee so that he will have to give his customers’ money back only 1% of the time? 1011.87 Tech: 1012.46 35. Radon: Radon is a naturally occurring radioactive substance that is found in the ground underneath many homes. Radon detectors are often placed in homes to determine whether radon levels are high enough to be dangerous. A radon level less than 4.0 picocuries is considered safe. Because levels fluctuate randomly, the levels measured by detectors are not exactly correct, but are instead normally distributed. It is known from physical theory that when the true level is 4.1 picocuries, the measurement made by a detector over a one-hour period will be normally distributed with mean 4.1 picocuries and standard deviation 0.2 picocurie. a. If the true level is 4.1, what is the probability that a one-hour measurement will be less than 4.0? 0.3085 b. If the true level is 4.1, would it be unusual for a one-hour measurement to indicate that the level is safe? No c. If a measurement is made for 24 hours, the mean will still be 4.1 picocuries, but the standard deviation will be only 0.04 picocurie. What is the probability that a 24-hour measurement will be below 4.0? 0.0062 d. If the true level is 4.1, would it be unusual for a 24-hour measurement to indicate that the level is safe? Yes 36. Electric bills: According to the U.S. Energy Information Administration, the mean monthly household electric bill in the United States in 2011 was $110.14. Assume the amounts are normally distributed with standard deviation $20.00. a. What proportion of bills are greater than $130? b. What proportion of bills are between $85 and $140? c. What is the probability that a randomly selected household had a monthly bill less than $120? 0.6879 Tech: 0.6890 37. Radon: Assume that radon measurements are normally distributed with mean 4.1 picocuries and standard deviation of 0.2. a. Find the 35th percentile of the measurements. b. Find the 92nd percentile of the measurements. c. Find the median of the measurements. 4.1 38. Electric bills: The U.S. Energy Information Agency reported that the mean monthly household electric bill in the United States in 2011 was $110.14. Assume the amounts are normally distributed with standard deviation $20.00. a. Find the 7th percentile of the bill amounts. 80.54 Tech: 80.62 b. Find the 62nd percentile of the bill amounts. c. Find the median of the bill amounts. 110.14
navidi_monk_elementary_statistics_2e_ch7-9
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