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Chapter 2: Q 47. (page 139)

Potato chips The weights of 9-ounce bags of a particular brand of potato

chips can be modeled by a Normal distribution with mean μ=9.12ounces and standard deviation σ=0.05ounce. Sketch the Normal density curve. Label the mean and the points that are 1,2, and 3 standard deviations from the mean.

Short Answer

Expert verified

Mean =9.12 ounce

Standard deviation =0.05 ounce

Step by step solution

01

Given information

Mean =9.12 ounce

Standard deviation =0.05 ounce

02

Calculation

For 68%

Within 1 standard deviation of the mean

μ−σ=9.12−0.05=9.07μ+σ=9.12+0.05=9.17

For 95%

Within 2 standard deviation of the mean

μ−2σ=9.12−2(0.05)=9.02μ+2σ=9.12+2(0.05)=9.22

For 99.7%

Within 3 standard deviations of the mean

μ−3σ=9.12−3(0.05)=8.97μ+3σ=9.12+3(0.05)=9.27

The graph is

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Most popular questions from this chapter

Are body weights Normal? The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. How about body weights? The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2pounds. The first and third quartiles are 118.3 pounds and 157.3pounds. Is it reasonable to believe that the distribution of body weights for women aged 20to 29 is approximately Normal? Explain

your answer.

Shopping spree The figure is a cumulative relative frequency graph of the amount spent by 50 consecutive grocery shoppers at a store.

a. Estimate the interquartile range (IQR) of this distribution. Show your method.

b. What is the percentile for the shopper who spent \(19.50?

c. Explain why the graph is steepest between \)10 and $30

Run fast Peter is a star runner on the track team. In the league championship meet, Peter records a time that would fall at the 80th percentile of all his race times that season. But his performance places him at the 50th percentile in the league championship meet. Explain how this is possible. (Remember that shorter times are better in this case!)

Blood pressure Larry came home very excited after a visit to his doctor. He announced proudly to his wife, “My doctor says my blood pressure is at the 90th percentile among men like me. That means I’m better off than about 90% of similar men.” How should his wife, who is a statistician, respond to Larry’s statement?

Outliers The percent of the observations that are classified as outliers by the 1.5×IQRrule is the same in any Normal distribution. What is this percent? Show your method clearly.
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