6-2 Real Applications of Normal Distributions 271 31. Aircraft Seat Width Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all adults. (Accommodating 100% of adults would require very wide seats that would be much too expensive.) Assume adults have hip widths that are normally distributed with a mean of 14.3 in. and a standard deviation of 0.9 in. (based on data from Applied Ergonomics). Find P99. That is, find the hip width for adults that separates the smallest 99% from the largest 1%. 32. Freshman 15 The term “Freshman 15” refers to the claim that college students typically gain 15 lb during their freshman year at college. Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of 2.6 lb and a standard deviation of 10.8 lb (based on Data Set 13 “Freshman 15”). Find the probability that a randomly selected male college student gains 15 lb or more during his freshman year. What does the result suggest about the claim of the “Freshman 15”? 33. Durations of Pregnancies The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a. In a letter to “Dear Abby,” a wife claimed to have given birth 308 days after a brief visit from her husband, who was working in another country. Find the probability of a pregnancy lasting 308 days or longer. What does the result suggest? b. If we stipulate that a baby is premature if the duration of pregnancy is in the lowest 3%, find the duration that separates premature babies from those who are not premature. Premature babies often require special care, and this result could be helpful to hospital administrators in planning for that care. 34. Body Temperatures Based on the sample results in Data Set 5 “Body Temperatures” in Appendix B, assume that human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. a. According to emedicinehealth.com, a body temperature of 100.4°F or above is considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.4°F is appropriate? b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 2.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.) 35. Designing Cars The sitting height of drivers must be considered in the design of a new car. The sitting height is measured from the seat to the top of the driver’s head, and adults have sitting heights that are normally distributed with a mean of 35.4 in. and a standard deviation of 1.8 in. (based on Data Set 3 “ANSUR II 2012”). Engineers have provided plans that can accommodate adults with sitting heights up to 38.9 in., but taller adults cannot fit. Find the percentage of adults with sitting heights that fit this car. Based on the result, is the engineering design feasible? 36. Water Taxi Safety When a water taxi sank in Baltimore’s Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a “worst-case” scenario in which all of the passengers are adult men. Assume that weights of men are normally distributed with a mean of 188.6 lb and a standard deviation of 38.9 lb (based on Data Set 1 “Body Data” in Appendix B). a. If one man is randomly selected, find the probability that he weighs less than 174 lb (the new value suggested by the National Transportation and Safety Board). b. With a load limit of 3500 lb, how many male passengers are allowed if we assume a mean weight of 140 lb? c. With a load limit of 3500 lb, how many male passengers are allowed if we assume the updated mean weight of 188.6 lb? d. Why is it necessary to periodically review and revise the number of passengers that are allowed to board?
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