Question

Potato chips The weights of $9-$ounce bags of a particular brand of potato

chips can be modeled by a Normal distribution with mean $\mu =9.12$ounces and standard deviation $\sigma =0.05$ounce. Sketch the Normal density curve. Label the mean and the points that are $1,2,$ and $3$ standard deviations from the mean.

Short answer

Mean $=9.12$ ounce

Standard deviation $=0.05$ ounce

Step-by-step solution

Given information

Mean $=9.12$ ounce

Standard deviation $=0.05$ ounce

Calculation

For $68\%$

Within $1$ standard deviation of the mean

$$\begin{gathered} \mu -\sigma =9.12-0.05=9.07 \\ \mu +\sigma =9.12+0.05=9.17 \end{gathered}$$

For $95\%$

Within $2$ standard deviation of the mean

$$\begin{gathered} \mu -2\sigma =9.12-2(0.05)=9.02 \\ \mu +2\sigma =9.12+2(0.05)=9.22 \end{gathered}$$

For $99.7\%$

Within $3$ standard deviations of the mean

$$\begin{gathered} \mu -3\sigma =9.12-3(0.05)=8.97 \\ \mu +3\sigma =9.12+3(0.05)=9.27 \end{gathered}$$

The graph is