Chapter 11.5, Problem 2CYU

To determine

To find: Percent of data that will be less than 361.

Answer to Problem 2CYU

16% of data lies under 361.

Explanation of Solution

Given information:

Mean: 416,

Standard deviation: 55.

Formula used:

Empirical Rule:

  

According to this rule:

• Around 68% of data falls in $1\sigma$ of the mean.
• Around 95% of data falls in $2\sigma$of the mean.
• Around 99.7% of data falls in $3\sigma$of the mean.

In the above figure, First half of the curve shows the amount of data that is below the mean, i.e. 50%,

Subtracting standard deviation from the mean,

  $\begin{array}{l}416-55=\mu -\sigma \\ 361=\mu -\sigma \end{array}$

As the empirical rule says that 34% data lies between $\mu -\sigma$ and $\mu$ , i.e. 361 and 416,

The amount of data that will lie below 361 will be,

  $\begin{array}{l}50\%-34\%\\ =\boxed{16\%}\end{array}$

16% of data lies under 361.