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Chapter 2: Q 3.1. (page 97)

Suppose that you convert the class鈥檚 heights from inches to centimeters (1inch=2.54cm). Describe the effect this will have on the shape, center, and spread of the distribution.

Short Answer

Expert verified

Centre and spread are affected but shape would not be changed

Step by step solution

01

Step 1. Given

02

Step 2. Concept

The following Minitab computer output validates the outcome: When each observation in distribution is standardized, the resultant set of z-scores has a mean of 0 and a standard deviation of 1

03

Step 3. Explanation

The change in height was from 1 inch to 2.54 centimeters. Height was modified from one centimeter to 2.54 inches based on the information provided. Multiplication has an effect on the center and spread, therefore spread and center would be multiplied by 2.54. The form would not be altered.

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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.

A uniform distribution The figure below displays the density curve of a uniform distribution. The curve takes the constant value 1 over the interval from 0

to 1 and is 0 outside the range of values. This means that data described by this distribution take values that are uniformly spread between 0 and 1

(a) Explain why this curve satisfies the two requirements for a density curve.

(b) What percent of the observations are greater than 0.8?

(c) What percent of the observations lie between0.25 and 0.75?

Use Table A to 铿乶d the value zfrom the standard Normal distribution that satis铿乪s each of the following conditions. In each case, sketch a standard Normal curve with your value of zmarked on the axis. Use your calculator or the Normal Curve applet to check your answers.

Working backward

(a) The 10th percentile.

(b) 34% of all observations are greater thanz.

The distribution of weights of 9-ounce bags of a particular brand of potato chips is approximately Normal with mean 渭=9.12ounces and standard deviation蟽=0.05ounces. Draw an accurate sketch of the distribution of potato chip bag weights. Be sure to label the mean, as well as the points one, two, and three standard deviations away from the mean on the horizontal axis.

R2.11 Fruit fly thorax lengths Here are the lengths in millimeters of the thorax for 49 male fruit flies: 18

Are these data approximately Normally distributed? Give appropriate graphical and numerical evidence to support your answer.

- Interpret a Normal probability plot.
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