statistics probability

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 62 ounces and a standard deviation of 7 ounces.

Use 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 48 and 69 ounces?  %

c) What percentage of the widget weights lie below 83 ?

Answer 1

a) 68% lie between 55 and 69, i.e. 62+/-7

b) 48 and 69 are 2 standard deviation below the mean and 1 above

68/2% above, 95/2% below. 34+47.5

= 81.5% between 48 and 69

c) 83-62 = 21 = 3 x7 = 3 standard deviations above the mean

99.7% lie between 3 standard deviations from the mean, by the empirical rule

(sometimes it's given as 99%, but 99.7% is more accurate)

.3/2% = .15% lie above 83

99.85% lie below 83