Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 61 ounces and a standard deviation of 7 ounces.

Use the Empirical Rule and a sketch of the normal distribution in order to answer the given question.

What percentage of the widget weights lie between 54 and 75 ounces?

Answer 1

Approximately 95% of the widget weights lie between 54 and 75 ounces.

Step-by-step explanation:

The question asks for the percentage of widget weights that lie between 54 and 75 ounces. We can use the Empirical Rule, which applies to bell-shaped distributions, to approximate this percentage. According to the Empirical Rule, approximately 68% of the data lies within one standard deviation of the mean, 95% lies within two standard deviations, and 99.7% lies within three standard deviations.

In this case, the mean weight of the widgets is 61 ounces and the standard deviation is 7 ounces. So, the range for one standard deviation below the mean to one standard deviation above the mean would be from 54 ounces to 68 ounces. The range for two standard deviations below the mean to two standard deviations above the mean would be from 47 ounces to 75 ounces.

Therefore, the percentage of widget weights that lie between 54 and 75 ounces is approximately 95%.