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.

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

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?

Business marketing publications.Business-to-business marketing describes the field of marketing between multiple business entities. The Journal of Business-to-Business Marketing (Vol. 15, 2008) produced a pie chart describing the number of business-to-business marketing articles published in all journals, by topical area, between 1971 and 2006. The data used to produce the pie chart are shown in the table.

Area

Number

Global Marketing

Sales Management

Buyer Behavior

Relationships

Innovation

Marketing Strategy

Channels/Distribution

Marketing Research

Services

235

494

478

498

398

280

213

131

136

Total

2,863

a.Compute the relative frequencies for the nine topical areas shown in the table. Interpret the relative frequency for Buyer Behavior.

b.Use the relative frequencies, part a, to construct a pie chart for the data. Why is the slice for Marketing Research smaller than the slice for Sales Management?

Cable TV subscriptions and “cord cutters.” 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 “cord cutters,” 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 “cord cutters.”

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?

Question: Corporate sustainability of CPA firms.Refer to the Business and Society(March 2011) study on the sustainability

behaviors of CPA corporations, Exercise 2.48 (p. 96). Numerical measures of variation for level of support for the 992 senior managers are shown in the accompanying Minitab printout.

Descriptive Statistics: Support

Variable

N

Mean

StDev.

Variance

Minimum

Maximum

Range

Support

992

67.755

26.871

722.036

0.000

155.000

155.000

a.Locate the range on the printout. Comment on the accuracy of the statement: “The difference between the largest and smallest values of level of support for the 992 senior managers is 155 points.”

b.Locate the variance on the printout. Comment on the accuracy of the statement: “On average, the level of support for corporate sustainability for the 992 senior managers is 722 points.”

c.Locate the standard deviation on the printout. Does the distribution of support levels for the 992 senior managers have more or less variation than another distribution with a standard deviation of 50? Explain.

d.Which measure of variation best describes the distribution of 992 support levels? Explain.

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