Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped with a mean of 37 ounces and a standard deviation of 3 ounces. Using the Empirical Rule, answer the following questions. Suggestion: Sketch the distribution.

a) 95% of the widget weights lie between  and

b) What percentage of the widget weights lie between 28 and 43 ounces?  %

c) What percentage of the widget weights lie below 40?  %

Answer 1

Solution :

Using Empirical rule,

P( - 1< X < + 1) = 68%

P( - 2< X < + 2) = 95%

P( - 3< X < + 3) = 99.7%

(a)

P( - 2< X < + 2) = 95%

P(37 - 2 * 3 < X 37 + 2 * 3) = 95%

P(31 < X < 43) = 95%

31 and 43

(b)

P(28 < X < 43) = P(X < 43) - P(X < 28) = 0.9985 - 0.975 = 2.35%

(c)

P(X < 40) = 84%