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Chapter 2: Q87E (page 113)

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鈥檛. 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鈥檚 decision?

Short Answer

Expert verified

The buyer will not buy the land.

Step by step solution

01

Illustrating the buyers' decision

According to the buyers' condition, at least 20% of the trees should be 40 feet tall. As the mean height of the trees is 30 feet, and the standard deviation is 3 feet, the measurement of 40 feet will fall to the right of the mean.

We do not know the distribution of height of the trees, so we will use the Chebyshev rule.

Upperrange=x炉+3s=30+3(3)=30+9=39Lowerrange=x炉-3s=30-3(3)=30-9=21

According to the rule, 88.88% of trees should fall between 21 and 39 feet.

The buyer needs at least 20% trees with 40 feet high, which is not possible as 40 lies after 39.

Therefore, the buyer will not buy the piece of land.

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Most popular questions from this chapter

Defects in new automobiles.Consider the following data from the automobile industry. All cars produced on a particular day were inspected for defects. The 145 defects found were categorized by type as shown in the accompanying table.

Defect Type

Number

Accessories

Body

Electrical

Engine

Transmission

50

70

10

5

10

a.Construct a Pareto diagram for the data. Use the graph to identify the most frequently observed type of defect.

b.All 70 car body defects were further classified as to type. The frequencies are provided in the following table. Form a Pareto diagram for the type of body defect. (Adding this graph to the original Pareto diagram of part a is called exploding the Pareto diagram.) Interpret the result. What type of body defect should be targeted for special attention?

Body Defect

Number

Chrome

Dents

Paint

Upholstery

Windshield

2

25

30

10

3

Calculate the mean for samples where

a.n=10,鈭�x=25b.n=16,鈭�x=400c.n=45,鈭�x=35d.n=18,鈭�x=242

Performance ratings of government agencies.The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, summer 2008). Evaluation scores ranged from 12 (lowest) to 60 (highest). The PARS evaluation scores for two consecutive years are shown in the next table.

a.Construct a scatterplot for the data. Do you detect atrend in the data?

b.Based on the graph, identify one or two agencies that hadgreater than expected PARS evaluation scores for year 2.

Question: In business, do nice guys really finish last?Do 鈥渘ice guys finish last鈥� in the competitive corporate world? In a study published in Nature(March 20, 2008), college students repeatedly played a version of the game 鈥減risoner鈥檚 dilemma,鈥� where competitors choose cooperation, defection, or costly punishment. (Cooperation meant paying 1 unit for the opponent to receive 2 units; defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times punishment was used against each player. A graph of the data

is shown in the accompanying scatterplot. Does it appear that average payoff is associated with punishment use? The researchers concluded that 鈥渨inners don鈥檛 punish.鈥� Do you agree? Explain.

Is honey a cough remedy?Refer to the Archives of Pediatrics and Adolescent Medicine(Dec. 2007) studyof honey as a remedy for coughing, Exercise 2.31 (p. 86). Recall that the 105 ill children in the sample wererandomly divided into three groups: those who receiveda dosage of over-the-counter cough medicine (DM),those who received a dosage of honey (H), and thosewho received no dosage (control group). The coughingimprovement scores (as determined by the children鈥檚parents) for the patients are reproduced in the nexttable.

Honey Dosage

12, 11, 15, 11, 10, 13, 10, 4 ,15, 16, 9, 14, 10, 6, 10, 8, 11, 12, 12, 8, 12, 9, 11, 15, 10, 15, 9, 13, 8, 12, 10, 8, 9, 5, 12

DM Dosage

4, 6, 9, 4, 7, 7, 7, 9, 12 ,10, 11, 6, 3, 4, 9, 12, 7, 6, 8, 12, 12, 4, 12, 13, 7, 10

No Dosage
(Control)

13, 9, 4, 4, 10, 15, 9, 5, 8, 6, 1, 0, 8, 12, 8, 7, 7, 1, 6, 7, 7, 12, 7, 9, 7, 9, 5, 11, 9, 5, 6, 8, 8, 6, 7, 10, 9, 4, 8, 7, 3, 1, 4, 3

a) Find the median improvement score for the honey dosage group.

b) Find the median improvement score for the DM dosage group.

c) Find the median improvement score for the control group.

d) Based on the results, parts a鈥揷, what conclusions can pediatric researchers draw? (We show how to support these conclusions with a measure of reliability in subsequent chapters.)
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