Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 60 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  and

b) What percentage of the widget weights lie between 53 and 74 ounces?  %

c) What percentage of the widget weights lie above 39 ?  %

Answer 1

Solution :

Using Empirical rule,

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

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

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

(a)

P(60 - 2 * 7 < X < 60 + 2 * 7) = 95%

P(46 < X < 74) = 95%

46 and 74

(b)

P(53 < X < 74) = 81.5%

(c)

P(X > 39) = 99.85%