/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q87E Land purchase decision.聽A buyer... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Professional athletes鈥� salaries.The salaries of superstar professional athletes receive much attention in the media. The multimillion-dollar long-term contract is now commonplace among this elite group. Nevertheless, rarely does a season pass without negotiations between one or more of the players鈥� associations and team owners for additional salary and fringe benefits for allplayers in their particular sports.

a.If a players鈥� association wanted to support its argument for higher 鈥渁verage鈥� salaries, which measure of central tendency do you think it should use? Why?

b.To refute the argument, which measure of central tendency should the owners apply to the players鈥� salaries? Why?

Museum management. Refer to the Museum Management and Curatorship (June 2010) study of how museums evaluate their performance, Exercise 2.14 (p. 74). Recall that managers of 30 contemporary art museums identified the performance measure used most often. A summary of the results is reproduced in the table. Consider the bar graph shown. Identify two ways the bar graph might mislead the viewer by overemphasizing the importance of one of the performance measures.

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.

Describe how the mean compares to the median for distribution as follows:

a.Skewed to the left

b.Skewed to the right

c.Symmetric

Question: Color and clarity of diamonds.Diamonds are categorized according to the 鈥渇our C鈥檚鈥�: carats, clarity, color, and cut. Each diamond stone that is sold on the open market is provided a certificate by an independent diamond assessor that lists these characteristics. Data for 308 diamonds were extracted from Singapore鈥檚 Business Times (Journal of Statistics Education, Vol. 9, No. 1, 2001). Color is classified as D, E, F, G, H, or I, while clarity is classified as IF, VVS1, VVS2, VS1, or VS2. In addition to color and clarity, the independent certification group (GIA, HRD, or IGI), the number of carats, and the asking price were recorded.

a.Use a graphical technique to summarize the color and clarity of the 308 diamond stones. What is the color and clarity that occurs most often? Least often?

b.Use a graphical method to describe the carat distribution of all 308 diamonds.

c.Use a graphical method to describe the carat distribution of diamonds certified by the GIA group.

d.Repeat part cfor the HRD and IGI certification groups.

e.Compare the three-carat distributions, parts cand d.Is there one particular certification group that appears to be assessing diamonds with higher carats than the others?

f.Find and interpret the mean of the data set.

g.Find and interpret the median of the data set.

h.Find and interpret the mode of the data set.

i.Which measures of central tendency best describe the 308-carat values? Explain.

j.Use the mean and standard deviation to form an interval that will contain at least 75% of the carat values in the data set.

k.Construct a scatter plot for the data, with a number of carats on the horizontal axis and price on the vertical axis. What type of trend do you detect?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.