Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget

weights have mean of 60 ounces and a standard deviation of 10 ounces.Use the Standard Deviation Rule, also known as the Empirical Rule.Suggestion: sketch the distribution in order to answer these questions.
a) 68% of the widget weights lie between
b) What percentage of the widget weights lie between 30 and 70 ounces?
c) What percentage of the widget weights lie below 80

Answer 1

a) 68% of the widget weights lie between 50 and 70 ounces.

b) Approximately 68% of the widget weights lie between 30 and 70 ounces.

c) About 84% of the widget weights lie below 80 ounces.

Step-by-step explanation:

a) According to the Standard Deviation Rule, approximately 68% of the data falls within one standard deviation of the mean. For a bell-shaped distribution with a mean of 60 ounces and a standard deviation of 10 ounces, this means that 68% of the widget weights lie between 50 (60 - 10) and 70 (60 + 10) ounces.

b) Extending the rule, we can determine that 95% of the data lies within two standard deviations of the mean. Therefore, approximately 68% of the widget weights lie between 30 (60 - 2 * 10) and 70 (60 + 2 * 10) ounces.

c) To find the percentage of widget weights below 80 ounces, we consider that 84% of the data lies within 1.5 standard deviations above the mean. So, about 84% of the widget weights lie below 80 (60 + 1.5 * 10) ounces.