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 6 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 99.7% of the widget weights lie between  and

b) What percentage of the widget weights lie between 57 and 81 ounces?  %

c) What percentage of the widget weights lie above 51 ?  %

Answer 1

Solution-A:

according to empirical rule

68% of the values lies within one standard deviation of the mean

(mean-sd =63-6 =57 and mean+sd=63+6=69)

95% of the values lies within two standard deviation of the mean

(mean-2sd=63-2*6=63-12=51 and 63+2*6=75)

99.7% of the values lies within three standard deviation of the mean

(mean-3sd=63-3*6=63-18=45 and 63+3*6=81)

a) 99.7% of the widget weights lie between

2.35+13.5+34+34+13.5+2.35=99.7%

P(a<X<b)=0.997

so 99.7% of the widget weights lie between

45 and 81

Solution-b:

P(57<X<81)

=34+34+13.5+2.35+0.15

=84%

84 percentage of the widget weights lie between 57 and 81 ounces

c) What percentage of the widget weights lie above 51 ?  %

P(X>51)

=13.5+34+34+13.5+2.35+0.15

=97.5%