Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 49 ounces and a standard deviation of 7 ounces. Use the Empirical Rule and a sketch of the normal distribution in order to answer these questions.

a) 68% of the widget weights lie between ___ and ____

b) What percentage of the widget weights lie between 28 and 56 ounces?  %

c) What percentage of the widget weights lie above 35 ?  %

Answer 1

Solution :

Given that,

mean = = 49

standard deviation = = 7

(A)Using Empirical rule,

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

P(49 - 1(7)< X < 49 +1(7)) =68%

P(42 < X < 56) =68%

answer =42 and 56

(B)= P(28< x <56 ) = P[(28 - 49) /7 < (x -) / < (56 - 49) /7 )]

= P( -3< Z < 1)

= P(Z <1 ) - P(Z < -3)

using Empirical rule

68% =  + / -1 = 68% / 2 = 34%

99.7% =  + / -1 = 99.7% / 2 = 49.85%

= P(Z <1 ) +P(Z < -3)

=34% +49.85%

=83.85%

(C)P(X >35) = 1 - P(X <35) = 1 - = 0.025= 97.5%