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Chapter 2: Q99. (page 117)

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.

Short Answer

Expert verified

The water customers are not at risk of drinking water with unhealthy lead levels.

Step by step solution

01

Defining percentile

A percentile is a value below which a certain number or percentage of values or observations fall. For example, the 45th percentile indicates 45 percent of the total number of values or observations can be found.

02

Indicating the reason for not having a risk of drinking water with unhealthy lead levels.

The research study shows that 90 percent of the samples show that the lead concentration is 0.00372 mg/L (which is less than 0.15 mg/L). Due to this reason, the drinking water is safe for the water customers.

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Most popular questions from this chapter

Rankings of research universities.Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 2.43 (p. 95). Recall that data on academic reputation score, financial aid awarded, and net cost to attend for the top 50 research universities are saved in the TOPUNIV file. The 50 academic reputation scores are listed in the accompanying table.

99 92 94 95 97 91 91 92 92 89 84 85 100 87 83 83 89 79 94 79 79 87 76 67 76 76 76 70 74 64 74 69 66 72 65 76 64 65 61 69 62 69 52 64 64 47 60 57 63 62

a.Find the median, lower quartile, and upper quartile for the data.

b.Find IQR for the data.

c.Graph the data with a box plot.

d.Do you detect any outliers? Suspect outliers?

Calculate the range, variance, and standard deviation for the following samples:

a.39, 42, 40, 37, 41

b.100, 4, 7, 96, 80, 3, 1, 10, 2

c.100, 4, 7, 30, 80, 30, 42, 2

Monitoring weights of flour bags.When it is working properly, a machine that fills 25-pound bags of flour dispenses an average of 25 pounds per fill; the standard deviation of the amount of fill is .1 pound. To monitor the performance of the machine, an inspector weighs the contents of a bag coming off the machine鈥檚 conveyor belt every half hour during the day. If the contents of two consecutive bags fall more than 2 standard deviations from the mean (using the mean and standard deviation given above), the filling process is said to be out of control, and the machine is shut down briefly for adjustments. The data

given in the following table are the weights measured by the inspector yesterday. Assume the machine is never shut down for more than 15 minutes at a time. At what times yesterday was the process shut down for adjustment? Justify your answer.

Time

Weight (pounds)

8:00 a.m

25.10

8:30

25.15

9:00

24.81

9:30

24.75

10:00

25.00

10:30

25.05

11:00

25.23

11:30

25.25

12:00

25.01

12:30 p.m

25.06

1:00

24.95

1:30

24.80

2:00

24.95

2:30

25.21

3:00

24.90

3:30

24.71

4:00

25.31

4:30

25.15

5:00

25.20

Construct a relative frequency histogram for the data summarized in the accompanying table.

Answer the following questions about the variability of data sets:

a.What is the primary disadvantage of using the range to compare the variability of data sets?

b.Describe the sample variance using words rather than a formula. Do the same with the population variance.

c.Can the variance of a data set ever be negative? Explain. Can the variance ever be smaller than the standard deviation? Explain.
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