Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.16 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains between 12.06 and 12.12 ounces.

The probability that the bottle contains between 12.06 and 12.12 ounces is 15.25%

Z score is given by:

From the normal distribution table, P(12.06 < x < 12.12) = P(-2.5 < z < -1) = P(z < -1) - P(z < -2.5) = 0.1587 - 0.0062 = 15.25%

The probability that the bottle contains between 12.06 and 12.12 ounces is 15.25%

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15.25% probability that the bottle contains between 12.06 and 12.12 ounces.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the probability that the bottle contains between 12.06 and 12.12 ounces.

This is the pvalue of Z when X = 12.12 subtracted by the pvalue of Z when X = 12.06. So

X = 12.12

has a pvalue of 0.1587

X = 12.06

has a pvalue of 0.0062

0.1587 - 0.0062 = 0.1525

15.25% probability that the bottle contains between 12.06 and 12.12 ounces.

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