I need help on math

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 ounces and a standard deviation of 5 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  and 

b) What percentage of the widget weights lie between 31 and 51 ounces?  %

c) What percentage of the widget weights lie below 56 ? 

Answer 1

a) 68% lie within 1 standard deviation of the mean, plus or minus 5 from 46, between 41 and 51

b) between 31 and 51 can be broken down to between 31 and 46 and 46 to 51, which is 3 standard deviations below and 1 standard deviation above. between 31 and 46 is half of 99.7 = 99.7/2 = 49.85% between 46 and 51 is half 68 = 68/2 = 34% add 34 + 49.85 =83.85 %

c) below 56 = 100 % - % above 56 =1-(.5-.95/2) = 1-(.5-.475) = 1-.025) =.975= 97.5%