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Chapter 2: Q.71 (page 135)

About what percent of the cockroaches have weights between 76 and 84 grams?

(a) 99.7%

(b) 95%

(c) 68%

(d) 47.5%

(e) 34%

Short Answer

Expert verified

The correct answer is (b)95%.

Step by step solution

01

Given Information

68-95-99.7 rule

Approximately 68% of the observations are within 1 standard deviation of the mean.

Approximately 95% of the observations are within 2 standard deviations of the mean.

Approximately 99.7% of the observations are within 3 standard deviations of the mean.

02

Explanation

Mean =80

Standard deviation =2

There is a 2standard deviation difference between 76and the mean.

(μ-2σ=80-2(2)=80-4=76)

There is a 2standard deviation difference between 84and the mean.

(μ+2σ=80+2(2)=80+4=84)

As a result of the 68-95-99.7 rule, approximately 95% of the data values fall within 2 standard deviations of the mean and thus approximately 95% of the cockroaches will be between 76 and 84 grams in weight.

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