Question

# he Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have...

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 ? %

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 or 97.5%