SOLUTION: Manufacturer A produces hammers that are normally distributed with a mean weight of 4.6 lb and a standard deviation of 0.8 lb. Manufacturer B produces hammers that are normally dis

Question 986146: Manufacturer A produces hammers that are normally distributed with a mean weight of 4.6 lb and a standard deviation of 0.8 lb. Manufacturer B produces hammers that are normally distributed with a mean weight of 6.3 lb and a standard deviation of 1.4 lb.
Which manufacturer is more likely to produce a hammer weighing exactly 5.2 lb? Explain.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The coefficient of variation is the ratio of the sd to the mean.
A: the coefficient is (0.8/4.6)=17.4%
B: the coefficient is (1.4/6.3)=22.2%
The desired weight is 3/4 of a sd above A and 0.786 sd below the mean in B. But because B has a greater variability relative to the mean, and variability matters a great deal in quality control, manufacturer A would be more likely.
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