Chapter 12.5, Problem 2CYP

To determine

Find the probability.

Answer to Problem 2CYP

  $97.5\%$ .

Explanation of Solution

Given information:

  

A randomly selected value in the distribution above is less than $49$ .

Calculation:

  

A normal distribution of data has a mean of $34$ with standard deviation of $5$ ,

The probability less than $49$ , is

  $\begin{array}{l}P\left(x<49\right)\\ \mu =34and\sigma =5\end{array}$

The probability that a randomly selected value in the distribution is less than

  $\begin{array}{l}\mu +2\sigma \\ 34+2\left(5\right)=44\end{array}$

  $44$ is the shaded area under the curve,

  $\begin{array}{l}P\left(x<49\right)=13.5+34+34+13.5+2+0.5\\ P\left(x<49\right)=97.5\%\end{array}$