Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped, The widget weights have a mean of 39 ounces and a standard deviation of 3 ounces, Use the Standard Deviation Rule, also known as the Empirical Rule.a) 99.7% of the widget weights lie between_____ and_____

Answer 1

The empirical rule states that 99.7% of the data observed following a normal distribution lies within 3 standard deviations of the mean.

Given data:

Mean: 39oz

Standard deviation: 3oz

Multiply the standard deviation by 3:

`3\sigma=3(3)=9`

Add and subtract the result above to the mean to get the interval of 99.7% of the data;

`\begin{gathered} 39-9=30 \\ 39+9=48 \end{gathered}`Then, the 97.7% of the widget weights lie between 30 ounces and 48 ounces