The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 39
ounces and a standard deviation of 10 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 9 and 49
ounces?
c) What percentage of the widget weights lie above 19
?
In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie in these ranges.
a) Mean = 39
SD = 10
68% = (39 - 10 and 39 + 10) = (29, 49)
b) 9 and 49 are 3 and 1 SD away
So, % = 99.73%/2 + 68.27%/2 = 84%
c) Above 19
That is above 2 standard deviations
% = 100% - 4.55%/2 = 97.725%
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