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Chapter 2: Q73E (page 110)
Question: For a set of data with a mound-shaped relative frequency distribution, what can be said about the percentage of the measurements contained in each of the intervals specified in Exercise 2.72?
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Motivation of athletes.A statistician keeps track of every serve that a player hits during the U.S. Open Tennis Championship. The statistician reports that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph.
a.Suppose the statistician also observes that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player’s serves was between 115 mph and 145 mph?
b.Consider the following serve speeds: 50 mph, 80 mph, and 105 mph. Using the z-score approach for detecting outliers, which of these would represent outliers in the distribution of the player’s serve speeds?
c.If nothing is known about the shape of the distribution, what percentage of the player’s serve speeds are less than 70 mph?
Jamming attacks on wireless networks. Refer to the International Journal of Production Economics (Vol. 172, 2016) study of U.S. military jamming attacks on wireless networks used by terrorists, Exercise 1.16 (p. 50). Recall that 80 recent jamming attacks were classified according to network type (WLAN, WSN, or AHN) attacked and number of channels (single- or multi-channel) of the network. The results are summarized in the accompanying table.
Network Type/ | Number of |
WLAN / Single | 31 |
WSN / Single | 13 |
AHN / Single | 8 |
WLAN / Multi | 14 |
WSN / Multi | 9 |
AHN / Multi | 5 |
Total | 80 |
a. Construct a Pareto diagram for the data. Interpret the results.
b. Construct a pie chart for network type only. Interpret the results.
A qualitative variable is measured for 20 companies randomly sampled and the data are classified into three classes, small (S), medium (M), and large (L), based on the number of employees in each company. The data (observed class for each company) are listed below. ______________________________________ SSL M SM M S M S L M S SSS M L S L ----------------------------------------------------------------
a. Compute the frequency for each of the three classes.
b. Compute the relative frequency for each of the three classes.
c. Display the results, part a, in a frequency bar graph.
d. Display the results, part b, in a pie chart.
STEM experiences for girls. The National Science Foundation (NSF) sponsored a study on girls’ 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—c 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?
Compare the z-scores to decide which of the following x values lie the greatest distance above the mean and the greatest distance below the mean.
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