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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’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?

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¯+3s=30+3(3)=30+9=39Lowerrange=x¯-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

Consider the following three measurements: 0, 4, and 12. Find the z-score for each measurement if they are from a population with the following mean and standard deviation equal to

a.µ = 2 and σ = 1

b.µ = 4 and σ = 2

c.µ = 8 and σ = 2

d.µ = 8 and σ = 8

Active nuclear power plants.Refer to Exercise 2.54 (p. 98) and the Nuclear Energy Institute’s data on the number of nuclear power plants operating in each of 30 states.

a.Find the range, variance, and standard deviation of this data set.

b.Eliminate the largest value from the data set and repeat part a.What effect does dropping this measurement have on the measures of variation found in part a?

c.Eliminate the smallest and largest value from the data set and repeat part a. What effect does dropping both of these measurements have on the measures of variation found in part a?

State

Status

Number of Power Plants

Alabama

Regulated

2

Arizona

Regulated

1

Arkansas

Regulated

1

California

Regulated

1

Connecticut

Deregulated

1

Florida

Regulated

3

Georgia

Regulated

2

Illinois

Deregulated

6

Iowa

Deregulated

1

Kansas

Regulated

1

Louisiana

Regulated

2

Maryland

Deregulated

1

Massachusetts

Deregulated

1

Michigan

Deregulated

3

Minnesota

Regulated

2

Mississippi

Regulated

1

Missouri

Regulated

1

Nebraska

Regulated

2

New Hampshire

Deregulated

1

New Jersey

Deregulated

3

New York

Deregulated

4

North Carolina

Regulated

3

Ohio

Deregulated

2

Pennsylvania

Deregulated

5

South Carolina

Regulated

4

Tennessee

Regulated

2

Texas

Deregulated

2

Virginia

Regulated

2

Washington

Regulated

1

Wisconsin

Deregulated

1

Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.

Using only integers between 0 and 10, construct two data sets with at least 10 observations each that have the same range but different means. Construct a dot plot for each of your data sets, and mark the mean of each data set on its dot diagram.

Question: The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 200 measurements are \(1,500 and \)300, respectively.

a.What are the units of measurement of the variable of interest? Based on the units, what type of data is this: quantitative or qualitative?

b.What can be said about the number of measurements between \(900 and \)2,100? Between \(600 and \)2,400? Between \(1,200 and \)1,800? Between \(1,500 and \)2,100?
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