Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 55 ounces and a standard deviation of 9 ounces.

Use the Empirical Rule, also known as the 68-95-99.7 Rule. Do not use Tables or Technology to avoid rounding errors.

Suggestion: sketch the distribution in order to answer these questions.

a) 68% of the widget weights lie between ?

b) What percentage of the widget weights lie between 37 and 64 ounces?  %

c) What percentage of the widget weights lie above 28 ?  %

Answer 1

a) According to rule of 68-95-99.7

68% of weights lie between

mean - std deviation to( mean std deviation)

= (55-9) to (55+9)

= (46 to 64 ) is where 68% lie

b)

37 to 64 = 55-2*9 to 55+9

= Mean - 2(std deviation) to (Mean + Std deviation)

According to empirical rule  

68% lie between mean - SD and (Mean +SD) and 95% lie between mean -2SD and mean +2SD which means

SD to 2SD has (95-68)/2 = 13.5%

Therefore 37 to 64 has 68%+13.5% =81.5% is the answer

c) According to empirical rule, 99.7% lie between mean -3SD and mean +3SD

28 = 55-3*9 = mean - 3SD

which tells amount that lie above 28= 99.7+(100-99.7)/2

= 99.85% is the answer to this question