Chapter 15, Problem 3CR

To determine

To find: The percent of the data is between $-3$ and $3$ , in a standard normal distribution.

Answer to Problem 3CR

The percent of the data is between $-3$ and $3$ is $99.74\%$ .

Explanation of Solution

Given information:

The given area is bounded by the $x$ and $y$ -axes and the line $x=3$ is $0.4987$ .

Calculation:

Calculate the percent of the data.

The standard normal curve is symmetrical about the $y$ -axis.

The area bound from the $y$ -axis $\left(x=0\right)$ to $x=3$ is the same as the area bound from $x=-3$ to the $y$ -axis.

The total area is twice the area form the $y$ -axis to $x=3$ .

Total area $=2\left(.04987\right)=.9974$

  $0.9974\times 100=99.74\%$

Therefore, the percent of the data is between $-3$ and $3$ is $99.74\%$ .