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Chapter 2: Q 35. (page 109)
Scores on the ACT college entrance exam follow a bell-shaped distribution with a mean and a standard deviation . Wayne鈥檚 standardized score on the ACT was What was Wayne鈥檚 actual ACT score?
The correct option is (c).
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What the mean means The figure below is a density curve. Trace the curve onto your paper.
(a) Mark the approximate location of the median. Justify your choice of location.
(b) Mark the approximate location of the mean. Justify your choice of location.
Use the 68-95-99.7 rule to estimate the percent of observations from a Normal distribution that fall in an interval involving points one, two, or three standard deviations on either side of the mean.
Measuring bone density Individuals with low bone density have a high risk of broken bones (fractures). Physicians who are concerned about low bone density (osteoporosis) in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual-energy X-ray absorptiometry (DEXA). A patient who undergoes a DEXA test usually gets bone density results in grams per square centimeterand in standardized units. Judy, who is years old, has her bone density measured using DEXA. Her results indicate a bone density in the hipand a standardized score of. In the reference population of For -year-old women like Judy, the mean bone density in the hip is
(a) Judy has not taken a statistics class in a few years. Explain to her in simple language what the standardized score tells her about her bone density.
(b) Use the information provided to calculate the standard deviation of bone density in the reference population.
Each year, about million college-bound high school juniors take the PSAT. In a recent year, the mean score on the Critical Reading test was and the standard deviation was. Nationally, of test takers earned a score of 65 or higher on the Critical Reading test鈥檚 to scale.9
PSAT scores Scott was one of junior boys to take the PSAT at his school. He scored on the Critical Reading test. This placed Scott at the 68th percentile within the group of boys. Looking at all boys鈥� Critical Reading scores, the mean was and the standard deviation was
(a) Write a sentence or two comparing Scott鈥檚 percentile among the national group of test-takers and among the boys at his school.
(b) Calculate and compare Scott鈥檚 z-score among these same two groups of test-takers.
T2.7. If the heights of American men follow a Normal distribution, and have heights between and , what is your estimate of the standard deviation of the height of American men?
(a)
(b)
(c)
(d)
(e)
If Mrs. Navard had the entire class stand on a -inch-high platform and then had the students measure the distance from the top of their heads to the ground, how would the shape, center, and spread of this distribution compare with the original height distribution? 
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