Chapter 11.1, Problem 10E

To determine

To calculate:

The probability value of the followings:

  $P\left(x\le \mu +\sigma \right)$

Answer to Problem 10E

The probability value of $P\left(x\le \mu +\sigma \right)$ is $2.5\%$ .

Explanation of Solution

Given information:

  $P\left(x\le \mu +\sigma \right)$

Calculation:

Know that:

The normal distribution curve of mean $\mu$ and standard deviation $\sigma$ is given as:

  

Now, the value of $P\left(x\le \mu +\sigma \right)$ is calculated as:

  $\begin{array}{l}P\left(x\le \mu +\sigma \right)=34\%+34\%+13.55\%+2.35\%+0.15\%\\ P\left(x\le \mu +\sigma \right)=84\%\end{array}$