Question

A bottler of soft drinks packages cans in six-packs. Suppose that the fill per can has an approximate normal distribution with a mean of 11 fluid ounces and a standard deviation of 0.3 fluid ounces.

(a)

What is the distribution of the total fill for a case of 24 cans? (Round your standard deviation to four decimal places.)

mean standard deviation

(b)

What is the probability that the total fill for a case is less than 261 fluid ounces? (Round your answer to four decimal places.)

(c)

If a six-pack of soda can be considered a random sample of size

* n* = 6

from the population, what is the probability that the average fill per can for a six-pack of soda is less than 10.6 fluid ounces? (Round your answer to four decimal places.)

Answer #1

Investigation: Soda six-packs
Most soda cans list the volume of soda as 12 fluid ounces. As with
all process, some variation occurs when filling soda cans. Suppose
that a company knows this and tries to over-fill cans a bit, so
that the actual volume of soda in a can follows a normal
distribution with mean 12.1 fluid ounces and standard deviation .15
fluid ounces.
a) What proportion of soda cans filled by this process will contain
less than 12 fluid...

Investigation: Soda six-packs
Most soda cans list the volume of soda as 12 fluid ounces. As
with all process, some variation occurs when filling soda cans.
Suppose that a company knows this and tries to over-fill cans a
bit, so that the actual volume of soda in a can follows a normal
distribution with mean 12.1 fluid ounces and standard deviation .15
fluid ounces.
e) Would the calculations in b) and/or c) be valid even if the
distribution of can...

Most soda cans list the volume of soda as 12 fluid ounces. As
with all process, some variation occurs when filling soda cans.
Suppose that a company knows this and tries to over-fill cans a
bit, so that the actual volume of soda in a can follows a normal
distribution with mean 12.1 fluid ounces and standard deviation .15
fluid ounces.
a) What proportion of soda cans filled by this process will
contain less than 12 fluid ounces? (In other...

An automated machine for a soft drink company is calibrated to
fill cans with 12-ounces of soda. Occasionally, the machine drifts
out of calibration and will not fill the cans with the correct
amount of soda. Suppose the machine goes out-of-calibration during
a batch run of 12,000. Technicians on site indicate that (about)
600 cans were underfilled before repairs could correct the problem.
Assume: x ≡ number of under-filled cans of soda in a randomly
selected six-pack. S ≡ a...

A soda company sells one of its soft drinks in 12 ounce cans. In
order to ensure that every can has at least 12 ounces in it, the
machines in the factory are set to fill each can with an average of
12.1 ounces of soda. Every week, a quality-control technician tests
10 cans to make sure that the average amount of soda in the cans is
still 12.1 ounces. If the conclusion of the test is that the number...

Suppose that the
number of ounces of soda put into a soft-drink can is normally
distributed with mean = 12.05 ounces and standard deviation = 0.03
ounce.
(a)
What fraction of cans will contain at least 12 ounces of
soda?
(b)
What fraction of cans will contain less than 11.9 ounces of
soda?
(c)
What fraction of cans will contain between 12 and 12.08 ounces
of soda?
(d)
One percent of all cans will weigh more than what value?

In 2008, the per capita consumption of soft drinks in Country A
was reported to be 18.97 gallons. Assume that the per capita
consumption of soft drinks in Country A is approximately normally
distributed, with a mean of 18.97 gallons and a standard deviation
of 5 gallons. Complete parts (a) through (d) below.
a. What is the probability that someone in Country A consumed
more than 12 gallons of soft drinks in 2008?
The probability is
(Round to four decimal...

In 2008, the per capita consumption of soft drinks in Country A
was reported to be 18.44 gallons. Assume that the per capita
consumption of soft drinks in Country A is approximately normally
distributed, with a mean of 18.44 gallons and a standard deviation
of 55 gallons. Complete parts (a) through (d) below.
a. What is the probability that someone in Country A consumed
more than 12 gallons of soft drinks in 2008?
The probability is
(Round to four decimal...

The fill amount in 1-liter soft drink bottles is normally
distributed, with a mean of 1.0 liter and a standard deviation of
0.05 liter. If bottles contain less than 95% of the listed net
content (0.95 liters, in this case), the manufacturer may be
subject to penalty by the state office of consumer affairs. Bottles
that have a net content above 1.08 liters may cause excess spillage
upon opening. In an effort to reduce the number of bottles that
contain...

A soft drink machine outputs a mean of 28 ounces per cup. The
machine's output is normally distributed with a standard deviation
of 3 ounces. What is the probability of filling a cup between 30
and 32 ounces? Round your answer to four decimal places.

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