Chapter 11.1, Problem 9E

To determine

To calculate:

The probability value of the followings:

  $P\left(x\ge \mu +2\sigma \right)$

Answer to Problem 9E

The probability value of $P\left(x\ge \mu +2\sigma \right)$ is $2.5\%$ .

Explanation of Solution

Given information:

  $P\left(x\ge \mu +2\sigma \right)$

Calculation:

Know that:

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

  

Now, the value of $P\left(x\ge \mu +2\sigma \right)$ is calculated as:

  $\begin{array}{l}P\left(x\ge \mu +2\sigma \right)=2.35\%+0.15\%\\ P\left(x\ge \mu +2\sigma \right)=2.5\%\end{array}$