Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 38 ounces and a standard deviation of 4 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 and b) What percentage of the widget weights lie between 26 and 46 ounces? % c) What percentage of the widget weights lie above 34 ? %

Answer 1

A) According to empirical rule, 95% of widget weight lie within first two standard deviation, I.e. ( mu -+ 2*sigma)

Where mu is mean and sigma is standard deviation.

38-2(4) and 38 +2(4)

30 and 46

Thus 95% of widget weight lies between 30 and 46 ounces.

B) Let X denote widget weight

P ( 26<X<46) = P( (26-38)/4 < Z < (46-38)/4)

= P(-3< Z< 2)

= 0.9759

Thus 97.59% of weight lie between 26 and 46 ounce.

C) P(X>34) = P( Z > (34-38)/4)

= P( Z > -1)

= 0.84134

Thus 84.13% of weight lie above 34