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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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Brush your teeth The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and standard deviation. Ricardo spends less than minute brushing his teeth about of the time. He spends more than minutes brushing his teeth of the time. Use this information to determine the mean and standard deviation of this distribution.
Shoes Refer to Exercise 1. Jackson, who reported owning 22 pairs of shoes, has a standardized score of z=1.10.
a. Interpret this z-score.
b. The standard deviation of the distribution of the number of pairs of shoes owned in this sample of 20 boys is 9.42. Use this information along with Jackson鈥檚 z-score to find the mean of the distribution.
Run fast! As part of a student project, high school students were asked to
sprint yards and their times (in seconds) were recorded. A cumulative relative frequency graph of the sprint times is shown here. 
a. One student ran the yards in seconds. Is a sprint time of seconds unusually slow?
b. Estimate and interpret the percentile of the distribution.
Potato chips Refer to Exercise About what percent of ounce bags of
this brand of potato chips weigh less than the advertised ounces? Is this likely to pose a problem for the company that produces these chips?
Measuring bone density Individuals with low bone density (osteoporosis) have a high risk of broken bones (fractures). Physicians who are concerned about low bone density in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual-energy ray absorptiometry (DEXA). The bone density results for a patient who undergoes a DEXA test usually are reported in grams per square centimeter () and in standardized units. Judy, who is years old, has her bone density measured using DEXA. Her results indicate bone density in the hip of 948 g/cm2 and a standardized score of The mean bone density in the hip is 956 in the reference population of year-old women like Judy.
a. Judy has not taken a statistics class in a few years. Explain to her in simple language what the standardized score reveals about her bone density.
b. Use the information provided to calculate the standard deviation of bone density in the reference population.
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