Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 ounces and a standard deviation of 7 ounces. Use the Empirical Rule. Standard Normal Curve with Empirical Values Suggestion: Sketch the distribution in order to answer these questions.

a) 95% of the widget weights lie between and
b) What percentage of the widget weights lie between 12 and 57 ounces? %
c) What percentage of the widget weights lie above 30 ? %

Answer 1

a) 95% of the widget weights lie between 29 and 57 ounces.

b) What percentage of the widget weights lie between 12 and 57 ounces? about 97.5%

c) What percentage of the widget weights lie above 30? about 97.5%

Explanation:

The empirical rule for a mean of 43 and a standard deviation of 7 is shown below.

a) 29 represents two standard deviations below the mean, and 57 represents two standard deviations above the mean, so, 95% of the widget weights lie between 29 and 57 ounces.

b) 22 represents three standard deviations below the mean, and the percentage of the widget weights below 22 is only 0.15%. We can say that the percentage of widget weights below 12 is about 0. Equivalently we can say that the percentage of widget weights between 12 an 43 is about 50% and the percentage of widget weights between 43 and 57 is 47.5%. Therefore, the percentage of the widget weights that lie between 12 and 57 ounces is about 97.5%

c) The percentage of widget weights that lie above 29 is 47.5% + 50% = 97.5%. We can consider that the percentage of the widget weights that lie above 30 is about 97.5%