Question

The Acme Company manufactures widgets. The distribution of widget weights is bell shaped. The widget weights have a means of 63 ounces and a standard deviation of 3 ounces
Use the empirical rule
a)95% of the widget lie between ___ and ___
b)what percentage of the widget lie between 60 and 69 ounces?
c) what percentage of the widget lie above 54?

Answer 1

(B)

• Here the 60 lies left to 1 sigma level (63 - 3) from the mean and the area covered by 1 sigma to the left is 47.5%
• ( As per empirical rule 1 sigma level represents the 68% of the area from the mean,
• this includes area from left and right as well.
• Hence here we considered only area from one side i
• only area from one side =95/2

= 47.5)

only area from one side =47.5

• Here the 69 lies in right to 2 sigma level ( 41 + 2*11)
• The 69 lies in right to 2 sigma level=41+22
• 69 lies in right to 2 sigma level= 66
• From the mean and the area covered by 2 sigma to the right is 47.5%
• ( As per empirical rule 2 sigma level represents the 95% of the area from the mean, this includes area from left and right as well.
• Hence here we considered only area from one side= 95/2
• Only area from another side = 47.5

the area from another side=47.5

• The total area covered = area from the one side + area from the another side = 47.5+47 = 95

The total area covered = 95%

The percentage of widget lies in between 60 and 69 is 95%