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Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 9 ounces.

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

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

a) 99.7% of the widget weights lie between  _ oz and  _ oz

b) What percentage of the widget weights lie between 41 and 77 ounces?  %

c) What percentage of the widget weights lie above 32 ?

Answer 1

a) mean 50 sd = 9

99.7 % lie between 3 sd's of the mean

3 sd's = 3x9 = 27, 50+/-27 = 77 and 23

99.7% are between 23 and 77, by the empirical rule

b) 41 and 77 are 1 sd below and 3 above

meaning 34% below and 99.7/2 = 49.85 % above

add them

34 +49.85 = 83.85% between 41 and 77, by the empirical rule

c) above 32

50-32/9 = 18/9 = 2 sd's

99.7 + (1-99.7)/2

= 99.7 +.3/2

= 99.7+ .15

= 99.85 % above 32