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Chapter 2: Q72E (page 110)
Question: For any set of data, what can be said about the percentage of the measurements contained in each of the following intervals?
a.xbar- sto xbar+ s
b.xbar- 2sto xbar+ 2s
c.xbar- 3sto xbar+ 3s
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Lead in drinking water. The U.S. Environmental Protection Agency (EPA) sets a limit on the amount of lead permitted in drinking water. The EPA Action Level for lead is .015 milligram per liter (mg/L) of water. Under EPA guidelines, if 90% of a water system’s study samples have a lead concentration less than .015 mg/L, the water is considered safe for drinking. I (coauthor Sincich) received a recent report on a study of lead levels in the drinking water of homes in my subdivision. The 90th percentile of the study sample had a lead concentration of .00372 mg/L. Are water customers in my subdivision at risk of drinking water with unhealthy lead levels? Explain.
Using only integers between 0 and 10, construct two data sets with at least 10 observations each that have the same range but different means. Construct a dot plot for each of your data sets, and mark the mean of each data set on its dot diagram.
Explain why we generally prefer the standard deviation to the range as a measure of variability for quantitative data.
Symmetric or skewed?Would you expect the data sets described below to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.
a.The salaries of all persons employed by a large university
b.The grades on an easy test
c.The grades on a difficult test
d.The amounts of time students in your class studied last week
e.The ages of automobiles on a used-car lot
f.The amounts of time spent by students on a difficult examination (maximum time is 50 minutes)
Consider the following sample of five measurements: 2, 1, 1, 0, 3.
a.Calculate the range, s2, and s.
b.Add 3 to each measurement and repeat part a.
c.Subtract 4 from each measurement and repeat part a.
d.Considering your answers to parts a, b, and c, what seems to be the effect on the variability of a data set by adding the same number to or subtracting the same number from each measurement?
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