Question

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 12.14 ounces and a standard deviation of 0.06 ounce.

a) Find the probability that the bottle contains fewer than 12.00 ounces of beer. Label the sketch of the normal curve with the values from the problem situation. Label the mean and the desired outcome. Use a z-score to find the probability. Round your answer to 2 decimal places.

b) Now that you have a probability that a bottle contains less than 12 ounces, what would be the probability that at least one bottle in a six pack would contain less than 12 ounces. Recall the probability of at least one from section 5-3, and a binomial distribution.

c) The brewery is concerned about the probability of a customer getting a bottle with less than 12 ounces. What could the brewery do that would lower the chance that a customer would get a bottle with less than 12 ounces?

Answer #1

**A) probability is calculated using Z table**

**b) binomial probability mass function is used with
parameter n= 6 & p= 0.01**

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
12.14 ounces and a standard deviation of 0.06 ounce.
a)Find the probability that the bottle contains fewer than 12.00
ounces of beer.Label the sketch of the normal curve with the values
from the problem situation. Label the mean and the desired outcome.
Use a...

3) 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 12.14 ounces and a standard deviation
of 0.06 ounce.
a) Find the probability that the bottle contains fewer than 12.00
ounces of beer.
Label the sketch of the normal curve with the values from the
problem
situation. Label the mean and the desired outcome....

A soft drink filling machine, when in perfect adjustment, fills
bottles with 12 ounces of soft drink. A random sample of 25 bottles
is selected, and the contents are measured. The sample yielded a
mean content of 11.88 ounces, with a sample standard deviation of
0.16 ounce.
Set up the hypotheses, and with a .05 level of significance,
test to see if the machine is in perfect adjustment. Show your
work.

A filling machine, when in proper adjustment, fills the bottles
with 32 ounces of liquid. A random sample of 19 bottles is
selected, and the contents are measured. The sample mean was 31.7
ounces, with a sample standard deviation of 0.55 ounces. With a
0.05 level of significance, test to see if the machine is in proper
adjustment. Assume the distribution of the population is
normal.

Question 3 Beer bottles are filled at an automated filling plant
so that the mean volume of beer is set at 330 ml. in each bottle.
From historic data, we know the volume of beer filled in a bottle
is normally distributed with a standard deviation of 4 ml.
Required of you:
a) What is the probability that a randomly selected bottle will
contain less than 325 ml?
b) What is the probability that a randomly selected 6-pack will
have...

A soft drink filling machine, when in perfect adjustment, fills
the bottles with 12 ounces of soft drink. A random sample of 49
bottles is selected, and the contents are measured. The sample
yielded a mean content of 11.88 ounces with a standard deviation of
0.35 ounces.
A) Specify the rejection region for = 0.01. Reject H0
if
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A local brewery distributes beer in bottles labeled 16.9 fluid
ounces. A government agency thinks that the brewery is cheating its
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of beer is less than 16.9 fluid ounces? Use a = 0.05.
a. State the...

A machine is designed to fill 16-ounce bottles of shampoo. When
the machine is working properly, the amount poured into the bottles
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If four bottles are randomly selected each hour and the number
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Hint: the standard deviation rule says
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(Cheating the consumer means selling less than what you are saying
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their contents, and obtains a mean of 31.7 ounces and a standard
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A) State the hypothesis.
B)...

8a. Means - A brewery distributes beer in bottles labeled 10
ounces. Some people think they are getting less than they pay for.
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