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Chapter 2: Q 86. (page 143)

The weights of laboratory cockroaches can be modeled with a Normal distribution having a mean of 80 grams and a standard deviation of 2 grams. The following figure is the Normal curve for this distribution of weights.

Point C on this Normal curve corresponds to

a. 84 grams.

b. 82 grams.

c. 78 grams.

d. 76 grams.

e. 74 grams.

Short Answer

Expert verified

The correct option is (c) 78grams

Step by step solution

01

Given information

Mean, 渭=80grams

Standard deviation, 蟽=2grams

02

Concept

Use of 68鈭�95鈭�99.7 rule

03

Explanation

According to 68鈭�95鈭�99.7 rule:

In a normal distribution, 68 percent of the data lies within 1 standard deviation of the mean.

A normal distribution has 95 percent of its data within two standard deviations of the mean.

A normal distribution has 99.7% of its data inside 1 standard deviation of the mean.

Then

The general Normal density graph is represented as:

Now,

We can see that Point C is located at 1 standard deviation below the mean on the Normal curve.

Then

The weight on corresponding Point C

xC=渭鈭�蟽=80grams鈭�2grams=78grams

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