Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 57 ounces and a standard deviation of 10 ounces.

Use 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 47 and 77 ounces?  %

c) What percentage of the widget weights lie above 27 ?  %

Answer 1

Given that, u = 57,0 =10 Empirical plot: 0.15% 2.35% 13.5% 34% -30 -20 -O 27 37 47 57 34% 13.5% 2.35% 0.15% o +20 +30 67 77 87 68% 95% 99.7% By using the above plot,

The 95% of the widget weights lie between 37 and 77. b) The percentage of the widget weights lies between 47 and 77 ounces is P(u-lo < X <u+ 20 ) = P(47< X <77) = 34% +34% +13.5% = 81.5% The percentage of the widget weights lie above 27 is, P(X > u-30)=P(X > 27) = 2.35%+13.5%+34%+34%+13.5%+2.35%+0.15% = 99.85%