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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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Cable TV subscriptions and 鈥渃ord cutters.鈥� Has the increasing popularity of smartphones and video streaming over the Internet affected cable and satellite TV subscriptions? This was one of the questions of interest in a recent Pew Research Center survey (December 2015). Telephone (both landline and cell phone) interviews were conducted on a representative sample of 2,001 adults living in the United States. For this sample, 1,521 adults reported that they currently receive cable or satellite TV service at home, 180 revealed that they have never subscribed to cable/satellite TV service at home, and the remainder (300 adults) admitted that they are 鈥渃ord cutters,鈥� i.e., they canceled the cable/satellite TV service. The results are summarized in the Minitab pie chart shown.
a. According to the pie chart, what proportion of the adults in the sample currently have a cable/satellite TV subscription at home? Verify the accuracy of this proportion using the survey results.
b. Now consider only the 1,821 adults in the sample that have at one time or another subscribed to cable/satellite TV service. Create a graph that compares the proportions of adults who currently subscribe to cable/satellite TV service with the proportion who are 鈥渃ord cutters.鈥�
In terms of percentiles, define QL, QM and QU
Using z-scores for grades. At one university, the students are given z-scores at the end of each semester rather than the traditional GPAs. The mean and standard deviation of all students鈥� cumulative GPAs, on which the z-scores are based, are 2.7 and .5, respectively.
a. Translate each of the following z-scores to the corresponding GPA: z = 2.0, z = -1.0, z = .5, z = -2.5.
b. Students with z-scores below 鈭�1.6 are put on probation. What is the corresponding probationary GPA?
c. The president of the university wishes to graduate the top 16% of the students with cum laude honors and the top 2.5% with summa cum laude honors. Where (approximately) should the limits be set in terms of z-scores? In terms of GPAs? What assumption, if any, did you make about the distribution of the GPAs at the university?
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鈥檚 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.
STEM experiences for girls. The National Science Foundation (NSF) sponsored a study on girls鈥� participation in informal science, technology, engineering, or mathematics (STEM) programs. The results of the study were published in Cascading Influences: Long-Term Impacts of Informal STEM Experiences for Girls (March 2013). The researchers sampled 174 young women who recently participated in a STEM program. They used a pie chart to describe the geographic location (urban, suburban, or rural) of the STEM programs attended. Of the 174 STEM participants, 107 were in urban areas, 57 in suburban areas, and 10 in rural areas.
a. Determine the proportion of STEM participants from urban areas.
b. Determine the proportion of STEM participants from suburban areas.
c. Determine the proportion of STEM participants from rural areas.
d. Multiply each proportion in parts a鈥攃 by 360 to determine the pie slice size (in degrees) for each location.
e. Use the results, part d, to construct a pie chart for the geographic location of STEM participants.
f. Interpret the pie slice for urban areas.
g. Convert the pie chart into a bar graph. Which, in your opinion, is more informative?
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