   Chapter 8.4, Problem 45E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Quality control The milk machine at a large dairy can be set to fill containers of various sizes. The fill amounts are normally distributed with the mean equal to the fill amount setting and a standard deviation of 0.3 oz. Find the fill amount setting so that the machine underfills a gallon container (128 oz) 1% of the time.

To determine

To calculate: The fill amount setting so that the machine underfills a gallon container (128 oz) 1% of the time if the milk machine at a large dairy can be set to fill containers of various sizes. The fill amounts are normally distributed with the mean equal to the fill amount setting and a standard deviation of 0.3 oz.

Explanation

Given Information:

The milk machine at a large dairy can be set to fill containers of various sizes. The fill amounts are normally distributed with the mean equal to the fill amount setting and a standard deviation of 0.3 oz.

Formula used:

If data for a population are normally distributed and σ is the standard deviation of the population data, then the number of standard deviations that x is from the mean μ is given by the z-score as;

z=xμσ

Calculation:

Consider that the following statement that the milk machine can be set to fill containers of various sizes.

Here it is normal distribution and the mean is equal to the fill amount setting and the standard deviation is;

σ=0.3

And the mean is equal to fill amount sitting which is 128 oz so;

μ=128

So, the probability is equal to 0.01 as;

Pr(zxμσ)=0.011Pr(zxμσ)=0

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