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Chapter 2: Q. 1.3 (page 114)
3. What percent of young women have heights between 62 and 72 inches? Show your work.
The percentage young women have heights between 62 and 72 inches are
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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’s 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’ Critical Reading scores, the mean was and the standard deviation was
(a) Write a sentence or two comparing Scott’s percentile among the national group of test-takers and among the boys at his school.
(b) Calculate and compare Scott’s z-score among these same two groups of test-takers.
Lynette, a student in the class, is inches tall. Find and interpret her z-score.
Growth charts We used an online growth chart to find percentiles for the height and weight of a -year-old girl who is inches tall and weighs pounds. According to the chart, this girl is at the percentile for weight and the percentile for height. Explain what these values mean in plain English.
T2.3. Rainwater was collected in water collectors at different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are and , respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding units to all of the values and then multiplying the result by . The mean and standard deviation of the corrected pH measurements are
(a)
(b)
(c)
(d)
(e)
R2.4 Aussie, Aussie, Aussie A group of Australian students were asked to estimate the width of their classroom in feet. Use the dot plot and summary statistics below to answer the following questions.
(a) Suppose we converted each student's guess from feet to meters . How would the shape of the distribution be affected? Find the mean, median, standard deviation, and IQR for the transformed data.
(b) The actual width of the room was feet. Suppose we calculated the error in each student's guess as follows: guess . Find the mean and standard deviation of the errors. How good were the students' guesses? Justify your answer.
Approximately locate the median (equal-areas point) and the mean (balance point) on a density curve.
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