What is the answer to this and can you explain it to me ?

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 61 ounces and a standard deviation of 7 ounces.

Use the Empirical Rule and a sketch of the normal 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 54 and 75 ounces?  %

c) What percentage of the widget weights lie below 82 ?

Answer 1

a) 61+ or - 2 standard deviations = 61 + or - 14: (47,75) 95% fall between 47 and 75

b) 54 to 75 is 61 -7 and 61+ 14. That's one standard deviation below the mean and two above the mean

34% are below (that's half of 68% from the empirical rule) and 47.5% above (half of 95%) Add them to get 34+47.5 = 81.5% between 54 and 75

c) 82 is 3 standard deviations above the mean: 61+3(7) = 61+21= 82. 99.7% are within 3 standard deviations from the mean, which is 49.85% above the mean to 82. Add 50% below the mean to get 99.85% less than 82.