SOLUTION: A brewery's filling machine is adjusted to fill bottles with a mean of 33.2 oz. of ale and a variance of 0.006. Periodically, a bottle is checked and the amount of ale noted. a)

Question 758249: A brewery's filling machine is adjusted to fill bottles with a mean of 33.2 oz. of ale and a variance of 0.006. Periodically, a bottle is checked and the amount of ale noted.
a) Assuming the amount of fill is normally distributed, what is the probability that the next randomly checked bottle contains more than 33.33 oz? (correct 4 decimals)
b) Let's say you buy 103 bottles of this ale for a party. How many bottles would you expect to find containing more than 33.33 oz. of ale? (correct whole number)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
answer for part a is .0984
answer for part b is .0984 * 103 = 10.1352 which is rounded to the nearest whole number of 10.
the distribution curve is shown below:
$$$$$

you were given the following information:

A brewery's filling machine is adjusted to fill bottles with a mean of 33.2 oz. of ale and a variance of 0.006. Periodically, a bottle is checked and the amount of ale noted.

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a) Assuming the amount of fill is normally distributed, what is the probability that the next randomly checked bottle contains more than 33.33 oz? (correct 4 decimals)

you set your mean at 33.2 ounces.
the standard deviation is equal to the square root of the variance which makes:
standard deviation = square root (.006) = .07746.
you set your standard deviation at .07746.
you check on "above" and enter 33.3 ounces in the box provided.
the calculator tells you that the area of the distribution curve greater than the value of 33.3 is equal to .0984.

this means that the probability of getting a bottle containing more than 33.3 ounces is equal to .0984.

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b) Let's say you buy 103 bottles of this ale for a party. How many bottles would you expect to find containing more than 33.33 oz. of ale? (correct whole number)

.0984 * 103 = 10.1352

round this to the nearest whole number and you get around 10 bottle out of every 103 would be expected to contain more than 33.3 ounces of beer.

the calculator i used can be found here:
http://davidmlane.com/normal.html

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