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Chapter 2: Q.68 (page 134)

Weights aren鈥檛 Normal The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. Weights, on the other hand, are not Normally distributed. The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third quartiles are 118.3 pounds and 157.3 pounds. What can you say about the shape of the weight distribution? Why?

Short Answer

Expert verified

The distribution is right-skewed.

Step by step solution

01

Given Information

The weights of women aged=20to29

Mean=141.7pounds

Median=133.2pounds

The first and third quartiles=118.3pounds

The third quartiles=157.3pounds

02

Explanation

Here are the steps to find the distribution of weights:

  • Due to the unequal mean and median, the shape of the weight distribution is skewed.
  • A right-skewed distribution is also evident since the mean is greater than the median and large values influence the mean.

In other words, the distribution of income is right-skewed.

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Most popular questions from this chapter

T2.1. Many professional schools require applicants to take a standardized test. Suppose that 1000 students take such a test. Several weeks after the test, Pete receives his score report: he got a 63, which placed him at the 73rd percentile. This means that

(a) Pete's score was below the median.

(b) Pete did worse than about 63%of the test takers.

(c) Pete did worse than about 73%of the test takers.

(d) Pete did better than about 63%of the test takers.

(e) Pete did better than about 73%of the test takers.

Computer use Mrs. Causey asked her students how much time they had spent using a computer during the previous week. The following figure shows a cumulative relative frequency graph of her students鈥� responses.

(a) At what percentile does a student who used her computer for 10hours last week fall?

(b) Estimate the median, Q1, and Q3from the graph. Are there any outliers

The distribution of heights of young women aged 18to 24is approximately N(64.5,2.5)

1. Sketch a Normal density curve for the distribution of young women's heights. Label the points one, two, and three standard deviations from the mean.
Now suppose that you convert the class鈥檚 heights to z-scores. What would be the shape, center, and spread of this distribution? Explain.

Use Table A to 铿乶d the proportion of observations from the standard Normal distribution that satis铿乪s each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question. Use your calculator or the Normal Curve applet to check your answers.

More Table A practice

(a) zis between 鈭�1.33and 1.65

(b) zis between 0.50and1.79
See all solutions

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