Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 54 ounces and a standard deviation of 8 ounces. Use the 68-95-99.7 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 and b) What percentage of the widget weights lie between 46 and 78 ounces? % c) What percentage of the widget weights lie below 70 ? %

Answer 1

Ans:

a)

99.7% of  the widget weights lie within 3 standard deviations of the mean.

So,

lower limit=54-3*8=30

upper limit=54+3*8=78

99.7% of the widget weights lie between 30 and 78.

b)

46 is one standard deviation below the mean and 78 is 3 standard deviations above the mean.

Percentage of the widget weights lie between 46 and 78 ounces=(68/2)+(99.7/2)=83.85%

c)

70 is 2 standard deviations above the mean.

Percentage of the widget weights lie below 70 is=100-2.5=97.5%