Chapter 11.5, Problem 1CYU

To determine

To find: The range of values that represent the middle $99.7\%$ of the distribution.

Answer to Problem 1CYU

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.

As the empirical rule states that Around 99.7% of data falls in $3\sigma$ of the mean,

So, the range of values that represent the middle $99.7\%$ of the distribution will be:

  $\begin{array}{l}\mu -3\sigma <X<\mu +3\sigma \\ =416-3\left(55\right)<X<416+3\left(55\right)\\ =416-165<X<416+165\\ =251<X<581\end{array}$

The range of values that represent the middle $99.7\%$ of the distribution is $251<X<581$ .