Chapter 11.3, Problem 2Q

To determine

To calculate:

The probability for $x$ in between $20$ and $32$ .

Answer to Problem 2Q

The probability when $20\le x\le 32$ is $84\%$ .

Explanation of Solution

Given information:

  $\begin{array}{l}\mu =32\\ \sigma =4\end{array}$

Calculation:

To determine the probability of a randomly selected $x$ -value from the standard normal distribution using the given information for $x$ in between $20$ and $32$ .

To find the probability when $20\le x\le 32$ , use the standard normal distribution as shown below:

  

Thus, the formula can be given as:

  $P\left(20\le x\le 32\right)=P\left(x-3\sigma \le x\le \sigma \right)$

Substitute the values in the above equation,

  $\begin{array}{l}P\left(20\le x\le 32\right)=34\%+13.5\%+2.35\%\\ P\left(20\le x\le 32\right)=49.85\%\end{array}$

Thus, the probability when $20\le x\le 32$ is $49.85\%$ .