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Chapter 2: Q. 42 (page 131)

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.

Short Answer

Expert verified

In order to draw a sketch of how potato chips are distributed, we can use the explanation below.

Step by step solution

01

Given Information

Mean =x炉=9.12ounces

Standard deviation =s=0.05ounce

Empirical rule for normal distribution

02

Explanation

In about 68%of the observations, the mean is within1standard deviation.

x炉-s=9.12-0.05=9.07x炉+s=9.12+0.05=9.17

In about95%of the observations, the mean is within 2standard deviation.

x炉-2s=9.12-2(0.05)=9.02x炉+2s=9.12+2(0.05)=9.22

In about99.7%of the observations, the mean is within3standard deviation.

x炉-3s=9.12-3(0.05)=8.97x炉+3s=9.12+3(0.05)=9.27

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Most popular questions from this chapter

T2.8. Which of the following is not correct about a standard Normal distribution?
(a) The proportion of scores that satisfy 0<z<1.5is 0.4332.
(b) The proportion of scores that satisfy z<-1.0is 0.1587.
(c) The proportion of scores that satisfy z>2.0is 0.0228.
(d) The proportion of scores that satisfy z<1.5is 0.9332.
(e) The proportion of scores that satisfyz>-3.0is 0.9938.

Questions T2.9 and T2.10 refer to the following setting. Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990swas 470and the standard deviation was 110. In 2009, the mean was 515and the standard deviation was 116 .
T2.10. Jane took the SAT in 1994and scored 500. Her sister Colleen took the SAT in 2009and scored 530. Who did better on the exam, and how can you tell?
(a) Colleen-she scored 30 points higher than Jane.
(b) Colleen-her standardized score is higher than Jane's.
(c) Jane-her standardized score is higher than Colleen's.
(d) Jane-the standard deviation was bigger in 2009.
(e) The two sisters did equally well-their z-scores are the same.

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?

About what percent of calls lasted less than 30 minutes? 30 minutes or more?

Old folks Here is a stem plot of the percent of residents aged 65 and older in the50states:

(a) Find and interpret the percentile for Colorado, which has 10.1%of its residents aged 65or older.

(b) Find and interpret the percentile for Rhode Island, with 13.9%of residents aged 65or older.

(c) Which of these two states is more unusual? Explain.
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