Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 45 ounces and a standard deviation of 6 ounces.

Use the Empirical Rule to answer the questions.

a) 99.7% of the widget weights lie between ? and    ? ounces.

b) What percentage of the widget weights lie between 33 and 63 ounces?  %

c) What percentage of the widget weights lie above 39 ounces? %   

Answer 1

Solution :

Given that ,

mean = = 45

standard deviation = = 6

a)

By using empirical rule,

- 3 = 45 - 3*6 = 27

and

+ 3 = 45 + 3*6 = 63

99.7% of the widget weights lie between 27 and 63 ounces.

b)

P( Between 33 and 63 once ) = P( Between 45 - 12 and 45 + 18 )

= 95% + 2.35%

= 97.35 %

97.35%  of the widget weights lie between 33 and 63 ounces.

c)

P( Above 39 ) = P( Above - )

= 68% + 13.5% + 2.35%

= 83.85%

83.85% of the widget weights lie above 39 ounces.