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?

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Mathematics

Chanel Walton

Today, 04:40

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?

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Hadassah · Answer 1

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