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Chapter 2: Q36. (page 94)
Calculate the mean for samples where
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Construct a scattergram for the data in the following table.
Variable 1: 174 268 345 119 400 520 190 448 307 252 Variable 2: 8 10 15 7 22 31 15 20 11 9 |
Land purchase decision.A buyer for a lumber company must decide whether to buy a piece of land containing 5,000 pine trees. If 1,000 of the trees are at least 40 feet tall, the buyer will purchase the land; otherwise, he won’t. The owner of the land reports that the height of the trees has a mean of 30 feet and a standard deviation of 3 feet. Based on this information, what is the buyer’s decision?
Voltage sags and swells. Refer to the Electrical Engineering (Vol. 95, 2013) study of transformer voltage sags and swells, Exercise 2.76 (p. 110). Recall that for a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184. Assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week. Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week.
a. Find the z-score for the number of sags for this transformer. Interpret this value.
b. Find the z-score for the number of swells for this transformer. Interpret this value.
Voltage sags and swells.Refer to the Electrical Engineering(Vol. 95, 2013) study of power quality (measured by“sags” and “swells”) in Turkish transformers, Exercise 2.96(p. 116). For a sample of 103 transformers built for heavyindustry, the mean and standard deviation of the numberof sags per week were 353 and 30, respectively; also, themean and standard deviation of the number of swells perweek were 184 and 25, respectively. Consider a transformerthat has 400 sags and 100 swells in a week.
a.Would you consider 400 sags per week unusual, statistically? Explain.
b.Would you consider 100 swells per week unusual, statistically? Explain.
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?
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