Chapter 6.1, Problem 28E

To determine

To find: probability $\text{P}\left(Y<31\right)$ and explain it

Answer to Problem 28E

  $\text{P}\left(Z<-1.67\right)=0.0475$

Explanation of Solution

Given:

  $\begin{array}{c}\mu =32\\ \sigma =0.6\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ =\frac{31-32}{0.6}\\ z=-1.67\end{array}$

  $\begin{array}{c}\text{P}\left(X\le 31\right)=\text{P}\left(Z<-1.67\right)=0.0475\\ =4.75\%\end{array}$

  

Probability for less than 31 is 0.0475 which imply that4.75 percent of the all bags have less than 31 ounces.