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)

µ = 12.14

σ = 0.06

P( X ≤ 12 ) = P( (X-µ)/σ ≤ (12-12.14)
/0.06)

**=P(Z ≤ -2.333 ) =
0.01**

b)

Sample size , n = 6

Probability of an event of interest, p = 0.01

X | P(X) | |

P ( X = 0) = C (6,0) * 0.01^0 * ( 1 - 0.01)^6= | 0 | 0.9415 |

P(atleast 1) = 1- P(0)

= 1 - 0.9415

**= 0.0585**

**c)**

brewery should decrese the standard deviation (for which they have to incresed the sample size)

**THANKS**

**revert back for doubt**

**please upvote**

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...

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.

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 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.

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
B) What is the conclusion

A local brewery distributes beer in bottles labeled 16.9 fluid
ounces. A government agency thinks that the brewery is cheating its
customers. The agency selects 31 of these bottles, measures their
contents, and obtains a sample mean of 16.71 fluid ounces and a
standard deviation of 0.51 fluid ounce. Does the sample show that
the government agency is correct in thinking that the mean amount
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
follows a normal distribution with mean 16.05 ounces with a
standard deviation of .2005 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?
Hint: the standard deviation rule says
that 95% of the observations are within how...

8a. Means - A brewery distributes beer in bottles labeled 10
ounces. Some people think they are getting less than they pay for.
The local Bureau of Weights and Measures randomly selects 70 of
these bottles, measures their contents and obtains a sample mean of
9.9 ounces. Assuming that σ is known to be 0.10 ounces, is it valid
at a 0.05 significance level to conclude that the brewery is
cheating the consumer?
8b. (Means) A bottling company distributes pop...

Beer bottles are filled so that they contain an average of 475
ml of beer in each bottle. Suppose that the amount of beer in a
bottle is normally distributed with a standard deviation of 8 ml.
a. What is the probability that a randomly selected bottle will
have less than 470 ml of beer? b. What is the probability that a
randomly selected 6-pack of beer will have a mean amount less than
470 ml?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 11 minutes ago

asked 21 minutes ago

asked 32 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 4 hours ago