The volume of apple juice in cans filled by a certain machine is normally distri

Question

The volume of apple juice in cans filled by a certain machine is normally distributed with mean 12.05 oz and standard deviation 0.03 oz. (a) What proportion of cans contain less than 12 oz of apple juice? (b) The mean volume of apple juice can be adjusted by calibrating the machine. If the standard deviation is fixed at 0.03 oz, to what value should the mean be set so that 99% of the cans will contain 12 oz or more of apple juice? (c) If instead we modify the standard deviation but fix the mean at 12.05 oz, to what value mast we set the standard deviation so that 99% of the cans will contain 12 oz or more of apple juice?

Explanation / Answer

as z=(X-mean)/std deviation

a)P(X<12)=P(Z<(12-12.05)/0.03)=P(Z<-1.667)=0.0478

b)for 99% ,z=-2.33

hence mean =12+2.33*0.03=12.07

c)for above std deviation =(12-12.05)/-2.33=0.0215

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