Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 63 ounces and a standard deviation of 5 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule.

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

b) What percentage of the widget weights lie between 53 and 78 ounces? %

c) What percentage of the widget weights lie below 68 ?

Answer 1

Solution :

Given that,

Using Empirical rule,

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

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

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

(a)

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

P(63 - 3 * 5< X < 63 + 3 * 5) = 99.7%

P(48 < X < 78) = 99.47%

48 and 78

(b)

P(53 < X < 78) = P(X < 78) - P(X < 53) = 0.997 - 0.0228 = 0.974

Answer = 97.4%

(c)

P(X < 68) = 0.84 = 84%

Answer = 84%