Question

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 ? %

Answer 1

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

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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%