Question

he 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 8 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 and

b) What percentage of the widget weights lie between 32 and 64 ounces? %

c) What percentage of the widget weights lie above 24 ? %

Answer #1

Ans:

Empirical rule says:

- 68% of data falls within the first standard deviation from the mean.
- 95% fall within two standard deviations.
- 99.7% fall within three standard deviations.

a)

lower limit=40-3*8=**16**

upper limit=40+3*8=**64**

99.7% of the widget weights lie between **16 and
64**

b)32 is one standard deviation below the mean and 64 is 3 standard deviation above the mean.

percentage of the widget weights lie between 32 and 64
ounces=(0.68/2)+(0.997/2)=0.8385 or **83.85%**

c)

24 is 2 standard deviation below the mean.

percentage of the widget weights lie above 24

percentage of the widget weights lie above 24
=(0.95/2)+(0.997/2)+0.0015=0.975 or **97.5%**

or using below figure:

=1-0.0235-(1-0.997)/2=0.975 o**r 97.5%**

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