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Chapter 2: Q. 41 (page 131)

The distribution of heights of adult American men is approximately Normal with mean 69inches and standard deviation of 2.5inches. Draw a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw the curve first, locate the points where the curvature changes, then mark the horizontal axis.)

Short Answer

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Here's a simple sketch of the distribution of men's heights based on the explanation below.

Step by step solution

01

Given Information

The American men has approximately mean 69inches and standard deviation 2.5inches.

02

Explanation

Normal distribution's Empirical rule is:

In about 68%of the observations, the mean is within 1standard deviation.

x炉鈭�s=69鈭�2.5=66.5x炉+s=69+2.5=71.5

In about 95% of the observations, the mean is within2standard deviation.

x炉-2s=69-2(2.5)=64x炉+2s=69+2(2.5)=74

In about 99.7%of the observations, the mean is within3standard deviation.

x炉-3s=69-3(2.5)=61.5x炉+3s=69+3(2.5)=76.5

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Most popular questions from this chapter

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.

Estimating SD The figure at top right shows two Normal curves, both with mean 0. Approximately what is the standard deviation of each of these curves?

If30 is added to every observation in a data set, the only one of the following that is not changed is

(a) the mean. (d) the standard deviation.

(b) the 75th percentile. (e) the minimum.

(c) the median.

Potato chips The distribution of weights of 9-ounce bags of a particular brand of potato chips is approximately Normal with a mean 渭=9.12ounces and standard deviation 伪=0.05ounce. 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. Use rule68-95-99.7.

a) What percent of bags weigh less than 9.02ounces?

(b) Between what weights do the middle 68%of bags fall?

(c) What percent of 9-ounce bags of this brand of potato chips weigh between 8.97and 9.17ounces?

(d) A bag that weighs9.07 ounces is at what percentile in this distribution?

R2.9 low-birth-weight babies Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year period. The distribution of birth weights is Normal with a mean of 3668 grams and a standard deviation of 511 grams. 17 Babies that weigh less than 2500 grams at birth are classified as "low birth weight."

(a) What percent of babies will be identified as having low birth weight? Show your work.

(b) Find the quartiles of the birth weight distribution. Show your work.
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