Question

In a bottle-filling process, the amount of drink injected into 16 oz bottles is normally distributed with a mean of 16 oz and a standard deviation of .02 oz. Bottles containing less than 15.95 oz do not meet the bottler’s quality standard. What percentage of filled bottles do not meet the standard?

Answer 1

Answer:

0.62

Step-by-step explanation:

We know that the amount of drink injected into 16 oz bottles is normally distributed with a mean of 16 oz and a standard deviation of .02 oz. The z-score associated to 15.95 is (15.95-16)/.02 = -2.5. Bottles containing less than 15.95 oz do not meet the bottles' quality standard, we compute the percentage of filled bottles that do not meet the standard using the z-score -2.5 and P(Z < -2.5) = 0.0062. Therefore, the percentage of filled bottles that do not meet the standard is 100(0.0062) = 0.62