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DRUGS R US is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.4. Assume the contents of the bottles are normally distributed. 4.23% of bottles will have more than how many ounces?

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Answer:

4.32% of the bottles will have more than 12.86 ounces.

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 6 ounces

Standard deviation = σ = 0.4 ounce

Let the z-score of 4.32% of the bottles be z' and the corresponding ounces be x'

The z-score for any is the value minus the mean then divided by the standard deviation.

z' = (x' - μ)/σ

P(x > x') = P(z > z') = 0.0432

Using the normal distribution table

P(z > z') = 1 - P(z ≤ z') = 0.0432

P(z ≤ z') = 1 - 0.0432 = 0.9568

z' = 1.715

1.715 = (x' - 6)/0.4

x' - 6 = 4(1.715)

x' = 6 + 6.86 = 12.86 ounces.

4.32% of the bottles will have more than 12.86 ounces.

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