Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 62 ounces and a standard deviation of 7 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

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

a) 95% of the widget weights lie between a and b

b) What percentage of the widget weights lie between 55 and 76 ounces?

c) What percentage of the widget weights lie above 41 %?

Answer 1

(A) using empirical rule with mean = 62 and standard deviation (sd) = 7

95% of data lies within 2 standad deviation from the mean

(B) 55 is one standard deviation below the mean

i.e., we can write 55 as 62-7 or 1 standard deviation below mean (34% of data will lie between mean and 55)

and

we can write 76 as 62+(2*7) or 2 standard deviation above mean (47.5 of data will lie between mean and 55)

so, total data values between 55 and 76 = 34% + 47.5% = 81.5%

(C) we can write 41 as mean - 3*sd

or 41 = 62 - 7*3

= 62 - 21

= 41

using empirical rule, only 0.15% of data lies below 41

so, 100-0.15 = 99.85% of data lies above 41