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A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 ounces with a standard deviation of .1005 ounces. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the means calculated should occur in what interval?

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jmonterrozar

Answer:

Between 15.95 ounces and 16.15 ounces.

Step-by-step explanation:

We have the following value m, being the mean, sd, being the standard deviation and n, the sample size:

m = 16.05

sd = 0.1005

n = 4

We apply the formula of this case, which would be:

m + - 2 * sd / (n ^ 1/2)

In this way we create a range, replacing we have:

16.05 + 2 * 0.1005 / (4 ^ 1/2) = 16.1505

16.05 - 2 * 0.1005 / (4 ^ 1/2) = 15.9495

Which means that 95% of all samples are between 15.95 ounces and 16.15 ounces.

the interval should be lies between 15.95 ounces and 16.15 ounces.

Calculation of the interval:

Since

Mean = 16.05

The standard deviation is 0.1005

And, the number should be 4

Here the following formula should be used.

[tex]m + - 2 \times sd \div (n ^ {1/2})[/tex]

So, it be like

[tex]16.05 + 2 \times 0.1005 \div (4 ^ {1/2}) = 16.1505\\\\16.05 - 2 \times 0.1005 \div (4 ^ {1/2}) = 15.9495[/tex][tex]16.05 + 2 \times 0.1005 \div (4 ^ {1/2}) = 16.1505\\\\16.05 - 2 \times 0.1005 \div (4 ^ {1/2}) = 15.9495[/tex]

Hence, the interval should be lies between 15.95 ounces and 16.15 ounces.

Learn more about mean here: https://brainly.com/question/24663100

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