Question

The distribution of weights of $9$-ounce bags of a particular brand of potato chips is approximately Normal with mean $\mu =9.12$ounces and standard deviation$\sigma =0.05$ounces. Draw an accurate sketch of the distribution of potato chip bag weights. Be sure to label the mean, as well as the points one, two, and three standard deviations away from the mean on the horizontal axis.

Short answer

In order to draw a sketch of how potato chips are distributed, we can use the explanation below.

Step-by-step solution

Given Information

Mean $=\overline{x}=9.12$ounces

Standard deviation $=s=0.05$ounce

Empirical rule for normal distribution

Explanation

In about $68\%$of the observations, the mean is within$1$standard deviation.

$$\begin{gathered} \overline{x}-s=9.12-0.05=9.07 \\ \overline{x}+s=9.12+0.05=9.17 \end{gathered}$$

In about$95\%$of the observations, the mean is within $2$standard deviation.

$$\begin{gathered} \overline{x}-2s=9.12-2(0.05)=9.02 \\ \overline{x}+2s=9.12+2(0.05)=9.22 \end{gathered}$$

In about$99.7\%$of the observations, the mean is within$3$standard deviation.

$$\begin{gathered} \overline{x}-3s=9.12-3(0.05)=8.97 \\ \overline{x}+3s=9.12+3(0.05)=9.27 \end{gathered}$$