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Chapter 2: Q 35. (page 108)
Scores on the ACT college entrance exam follow a bell-shaped distribution with mean and standard deviation 5. Wayne鈥檚 standardized score on the ACT was What was Wayne鈥檚 actual ACT score?
a.
b.
c. 1
d.
e.
The correct option is (d)
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Post office A local post office weighs outgoing mail and finds that the weights of first-class letters are approximately Normally distributed with a mean of ounces and a standard deviation of ounces.
a. Estimate the 60th percentile of first-class letter weights.
b. First-class letters weighing more than ounce require extra postage. What proportion of first-class letters at this post office requires extra postage?
The army reports that the distribution of head circumference among male soldiers is approximately Normal with mean of inches and standard deviation inches.
(a) A male soldier whose head circumference is -inches would be at what percentile? Show your method clearly.
(b) The army鈥檚 helmet supplier regularly stocks helmets that fit male soldiers with head circumferences between and inches. Anyone with a head circumference outside that interval requires a customized helmet order. What percent of male soldiers require custom helmets? Show your work, including a well-labeled sketch of a Normal curve.
(c) Find the interquartile range for the distribution of head circumference among male soldiers. Show your method clearly.
Potato chips The weights of ounce bags of a particular brand of potato
chips can be modeled by a Normal distribution with mean ounces and standard deviation ounce. Sketch the Normal density curve. Label the mean and the points that are and standard deviations from the mean.
Used cars, cheap! A used-car salesman has 28 cars in his inventory, with prices ranging from \(11,500 to \)25,000. For a Labor Day sale, he reduces the price of each car by $500. What effect will this reduction have on each of the following characteristics of the resulting distribution of price?
a. Shape
b. Mean and median
c. Standard deviation and interquartile range (IQR)
Put a lid on it! Refer to Exercise . The supplier is considering two changes to reduce the percent of its large-cup lids that are too small to less than . One strategy is to adjust the mean diameter of its lids. Another option is to alter the production process, thereby decreasing the standard deviation of the lid diameters.
(a) If the standard deviation remains at inches, at what value should the supplier set the mean diameter of its large-cup lids to ensure that less than are too small to fit? Show your method.
(b) If the mean diameter stays at inches, what value of the standard deviation will result in less than of lids that are too small to fit? Show your method.
(c) Which of the two options in (a) and (b) do you think is preferable? Justify your answer. (Be sure to consider the effect of these changes on the percent of lids that are too large to fit.)
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