Question
In: Statistics and Probability
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have...
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 40 ounces and a standard deviation of 9 ounces. Use the Empirical Rule, find a) 99.7% of the widget weights lie between and b) What percentage of the widget weights lie between 22 and 67 ounces? % c) What percentage of the widget weights lie below 49 ? %
Solutions
Expert Solution
Mean = 
= 40
Standard deviation = 
= 9
Empirical rule:
1) About 68% of data lies in the 1 standard deviation from the mean.
that is in the interval.
2) About 95% of data lies in the 2 standard deviations from the mean.
that is in the interval 
3) About 99.7% data lies in the 3 standard deviation from the mean.
that is in the interval 
-------------------------------------------------------------------------------------------------------------
a)
About 99.7% data lies in the 3 standard deviation from the mean.
that is in the interval
b) 22 = 40 - 2*9 = 
67 = 40 + 3*9 = 
The percentage of the widget weights lie between 22 and 67 ounces is
0.5*95% + 0.5*99.7% = 97.35%
c) 49 = 40 + 9 = 
The percentage of the widget weights lie below 49 is
50% + 
68%= (50+34)%=84%
orchestra answered 2 years agoRelated Solutions
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