Mathematics, 27.03.2020 01:52 YeetMyFeet

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.

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Answer from: jonathanmontalv

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

Z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation\\\\\\Given\ that\ \mu=12.16,\sigma=0.04\\\\\\a) For\ x=12.06:\\\\z=\frac{12.06-12.16}{0.04}=-2.5\\\\For \ x=12.12:\\\\z=\frac{12.12-12.16}{0.04}=-1$

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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Answer from: demarcuswiseman

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 $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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:

$\mu = 12.16, \sigma = 0.04$

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

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{12.12 - 12.16}{0.04}$

Z = -1

Z = -1 has a pvalue of 0.1587

X = 12.06

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{12.06 - 12.16}{0.04}$

Z = -2.5

Z = -2.5 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.

Answer from: Quest

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

Answer from: Quest

a natural event such as a flood, earthquake, or hurricane that causes great damage or loss of life.

step-by-step explanation:

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Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the am...

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