Empirical Rule need help

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 51 ounces and a standard deviation of 7 ounces.

Use the Empirical Rule, find

a) 68% of the widget weights lie between  and 

b) What percentage of the widget weights lie between 37 and 58 ounces?  %

c) What percentage of the widget weights lie below 72 ?  %

Suggestion: sketch the distribution in order to answer these questions.

Answer 1

a) 68% is 44 to 58 ounces

between 51 + and - 7 = 44 ounces to 58 ounces

b) 37 to 58 is 80.5%

(51-37)/7 = 14/7 = 2 standard deviations. and (58-51)/7 = 7/7 = one standard devation

half of 95% to the left = 47.5%, half of 68% to the right = 34%. 47.5+34 = 80.5% between 37&58

c) below 72 is 0.3%

(72-51)/7 = 21/7 = 3 standard deviations below the mean. That means 1-99.7 = 0.3%