Use the Standard Deviation Rule, also known as the Empirical Rule.

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 65 ounces and a standard deviation of 6 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

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 59 and 77 ounces?  __ %

c) What percentage of the widget weights lie above 47 ? ___%

Answer 1

Empirical Rule is 64-95-99 for 1, 2 and 3 standard deviations from the mean

If mean is 65 and standard deviation is 6, then 68% of the weights will be between 59 and 71

95% will be between 53 and 77

99.7% will be between 47 and 83, with 0.3% in the tails, and 0.15% in each tail

above 47 will be 100%-0.15% = 99.85%

a) 53 and 77

b) 95%

c) 99.85%