91Ó°ÊÓ

A company that manufactures rivets believes the shear strength (in pounds) is modeled by \(N(800,50)\) a. Draw and label the Normal model. b. Would it be safe to use these rivets in a situation requiring a shear strength of 750 pounds? Explain. c. About what percent of these rivets would you expect to fall below 900 pounds? d. Rivets are used in a variety of applications with varying shear strength requirements. What is the maximum shear strength for which you would feel comfortable approving this company's rivets? Explain your reasoning.

More IQs In the Normal model \(N(100,15)\) from Exercise 10 ?, what cutoff value bounds a. the highest \(5 \%\) of all IQs? b. the lowest \(30 \%\) of the IQs? c. the middle \(80 \%\) of the IQs?

Cattle, finis Consider the Angus weights model \(N(1152,84)\) one last time. a. What weight represents the 40th percentile? b. What weight represents the 99th percentile? c. What's the IQR of the weights of these Angus steers?

IQ, finis Consider the IQ model \(N(100,15)\) one last time. a. What IQ represents the 15 th percentile? b. What IQ represents the 98th percentile? c. What's the IQR of the IQs?

Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of \(188 \mathrm{mg} / \mathrm{dL}\) and a standard deviation of \(24 .\) a. Draw and label the Normal model. b. What percent of adult women do you expect to have cholesterol levels over \(200 \mathrm{mg} / \mathrm{dL} ?\)

A tire manufacturer believes that the treadlife of its snow tires can be described by a Normal model with a mean of 32,000 miles and standard deviation of 2500 miles. a. If you buy one of these tires, would it be reasonable for you to hope it will last 40,000 miles? Explain. b. Approximately what fraction of these tires can be expected to last less than 30,000 miles? c. Approximately what fraction of these tires can be expected to last between 30,000 and 35,000 miles? d. Estimate the IQR of the treadlives. e. In planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the dealer does not want to take too big a risk. If the dealer is willing to give refunds to no more than 1 of every 25 customers, for what mileage can he guarantee these tires to last?

Companies that design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 38.2 inches and standard deviation of 1.8 inches. a. What fraction of kindergarten kids should the company expect to be less than 3 feet tall? b. In what height interval should the company expect to find the middle \(80 \%\) of kindergarteners? c. At least how tall are the biggest \(10 \%\) of kindergarteners?

Most people think that the "normal" adult body temperature is \(98.6 \circ \mathrm{F}\) That figure, based on a 19th-century study, has recently been challenged. In a 1992 article in the Journal of the American Medical Association, researchers reported that a more accurate figure may be \(98.2 \circ \mathrm{F}\). Furthermore, the standard deviation appeared to be around \(0.7 \circ \mathrm{F}\). Assume that a Normal model is appropriate. a. In what interval would you expect most people's body temperatures to be? Explain. b. What fraction of people would be expected to have body temperatures above \(98.6 \circ \mathrm{F}\) c. Below what body temperature are the coolest \(20 \%\) of all people?