Chapter 2.2, Problem 86E

To determine

Weight of laboratory cockroach at corresponding Point C on the Normal curve.

Answer to Problem 86E

Point C on the normal curve corresponds to 78 grams.

Explanation of Solution

Given information:

  

Mean, $\mu =80\text{grams}$

Standard deviation, $\sigma =2\text{grams}$

Calculations:

According to 68 − 95 − 99.7 rule:

68% of the data of a normal distribution lies with 1 standard deviation from the mean.

95% of the data of a normal distribution lies with 2 standard deviation from the mean.

99.7% of the data of a normal distribution lies with 1 standard deviation from 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.

  $\begin{array}{l}{x}_{\text{C}}=\mu -\sigma \\ =80\text{grams}-2\text{grams}\\ =78\text{grams}\end{array}$