Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped with a mean of 54 ounces and a standard deviation of 4 ounces. Using the Empirical Rule, answer the following questions. Suggestion: Sketch the distribution.

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

b) What percentage of the widget weights lie between 46 and 66 ounces? %

c) What percentage of the widget weights lie below 58? %

Answer 1

Solution :

Using Empirical rule,

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

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

(a)

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

P(54 - 3 * 4 < X < 54 + 3 * 4) = 99.%

P(42 < X < 66) = 99.7%

42 and 66

(b)

P(46 < X < 66) = P(X < 66) - P(X < 46) = 0.9985 - 0.975 = 2.35%

C)

P(X < 58) = 84%