Question

The weight of a bag of potato chips is stated as 300 g. The amount that the packaging machine puts in each bag is normally distributed with mean 306 g and standard deviation 3.6 g. (a) (4 points) What is the proportion of all bags sold that are underweight? (b) (3 points) A ”bargain pack” contains two bags. Find the probability that both are underweight. (c) (5 points) Find the probability that the average weight of the bags in a bargain pack is below 300 g.

Answer #1

Mean, = 306 g

Standard deviation, = 3.6 g

Let X denote the weight of a randomly selected bag of potato chips

(a) The proportion of all bags sold that are underweight

= P(X < 300)

= P{Z < (300 - 306)/3.6}

= P(Z < -1.667)

= 0.0478 = 4.78%

(b) The probability that both the bag are underweight

= = 0.0023

(c) The sampling distribution of the average weight of the bags in a bargain pack has Mean = 306 g

and standard deviation = 3.6/√2 = 2.546

The probability that the average weight of the bags in a bargain pack is below 300 g = P( < 300)

= P{Z < (300 - 306)/2.546}

= P(Z < -2.357)

= 0.0092

The weight of potato chips in a medium-size bag is stated to be
10 ounces. The amount that the packaging machine puts in these bags
is believed to have a normal model with a mean of 10.2 ounces and a
standard deviation of 0.14 ounces.
a) What fraction of all bags sold are underweight?
b) Some of the chips are sold in "bargain packs" of 5 bags.
What's the probability that none of the 5 is underweight?
c) What's...

The weight of potato chips in a largelarge-size bag is stated
to be 16 ounces. The amount that the packaging machine puts in
these bags is believed to have a normal model with a mean of 16.3
ounces and a standard deviation of 0.17ounces. a) What fraction of
all bags sold are underweight? b) Some of the chips are sold in
"bargain packs" of 3 bags. What's the probability that none of the
3 is underweight? c) What's the probability...

The weight of potato chips in a largelarge-size bag is stated
to be 20 ounces. The amount that the packaging machine puts in
these bags is believed to have a normal model with a mean of 20.1
ounces and a standard deviation of 0.09 ounces. a) What fraction
of all bags sold are underweight? b) Some of the chips are sold
in "bargain packs" of 3 bags. What's the probability that none of
the 3 is underweight? c) What's the...

The weight of potato chips in a small-size bag is stated to be
5 ounces. The amount that the packaging machine puts in these bags
is believed to have a normal model with a mean of
5.1 ounces and a standard deviation of 0.09 ounces.
a) What fraction of all bags sold are underweight?
b) Some of the chips are sold in "bargain packs" of 5bags.
What's the probability that none of the 5 is underweight?
c) What's the probability...

The weight of cement in a large-size bag is stated to be 16 kg.
The amount that the packaging machine puts in these bags is
believed to have a normal model with a mean of 16.2kg and a
standard deviation of 0.14 kg.
a) What fraction of all bags sold are underweight?
b) Some of the cement is sold in "bargain packs" of 5 bags.
What's the probability that none of the 5 is underweight?
c) What's the probability that...

The mean weight of a bag of potato chips from Potato Chip
Incorporated is 14.75 ounces with a standard deviation of 0.4
ounces. A sample of 100 bags of potato chips has a mean weight of
w.
(a) Assuming the weight of potato chip bags is normally
distributed, what is the mean and standard deviation of the
variable w?
(b) Assuming the weight of potato chip bags has a distribution of
unknown shape, what is the mean and standard deviation...

A manufacturer of potato chips would like to know whether its
bag filling machine works correctly at the 402 gram setting. It is
believed that the machine is underfilling or overfilling the bags.
A 13 bag sample had a mean of 409 grams with a standard deviation
of 13 Assume the population is normally distributed. A level of
significance of 0.1 will be used. Specify the type of hypothesis
test.

A manufacturer of potato chips would like to know whether its
bag filling machine works correctly at the 419419 gram setting. Is
there sufficient evidence at the 0.010.01 level that the bags are
overfilled? Assume the population is normally distributed.
State the null and alternative hypotheses for the above
scenario.

4. The number of chocolate chips in an 18-ounce bag of Chips
Ahoy! cookies is approximately normally distributed with a mean of
µ = 1262 chips and standard deviation σ = 188 chips. Source: Brad
Warner and Jim Rutledge, Chance, 12(1): 10-14, 1999
(a) (3 points) What is the probability that a randomly selected
18-ounce bag of Chips Ahoy! contains between 1000 and 1400
chocolate chips, inclusive? Round your answer to 4 decimal places.
Problem 4 continued:
(b) (3 points)...

A manufacturer of potato chips would like to know whether its
bag filling machine works correctly at the 409 gram setting. It is
believed that the machine is underfilling the bags. A 20 bag sample
had a mean of 399 grams with a standard deviation of 21. Assume the
population is normally distributed. A level of significance of 0.02
will be used. Find the P-value of the test statistic. You may write
the P-value as a range using interval notation,...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 15 minutes ago

asked 48 minutes ago

asked 1 hour 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 3 hours ago