Question

An advertiser claims that the average percentage of brown M&M'S candies in a package of milk chocolate M&M'S is 14%. Suppose you randomly select a package of milk chocolate M&M'S that contains 54 candies and determine the proportion of brown candies in the package.

(a) What is the approximate distribution of the sample proportion of brown candies in a package that contains 54 candies?

The distribution is approximated by a normal distribution with mean 0.14 and standard deviation 0.86.The distribution is approximated by a normal distribution with mean 14 and standard deviation 0.0472. The distribution is approximated by a normal distribution with mean 7.6 and standard deviation 756.The distribution is binomial and cannot be approximated.The distribution is approximated by a normal distribution with mean 0.14 and standard deviation 0.0472.

(b) What is the probability that the sample percentage of brown
candies is less than 20%? (Round your answer to four decimal
places.)

(c) What is the probability that the sample percentage exceeds 33%?
(Round your answer to four decimal places.)

(d) Within what range would you expect the sample proportion to lie
about 95% of the time? (Round your answers to two decimal
places.)

Answer #1

According to the M&M® website, the average percentage of
brown M&M® candies in a package of milk chocolate M&Ms is
12%. (This percentage varies, however, among the different types of
packaged M&Ms.) Suppose you randomly select a package of milk
chocolate M&Ms that contains 60 candies and determine the
proportion of brown candies in the package.
(a) What is the approximate distribution of the sample
proportion of brown candies in a package that contains 60
candies?
i. The distribution is...

According to M&Ms Web site, each package of the milk
chocolate candies typically contain 14% brown, 13% red, 14% yellow,
16% green, 24% blue, and 20% orange M&Ms. You go to the store
and buy a standard-sized package. When you open it, you find that
it contains 51 M&Ms, distributed as follows: Color Brown Red
Yellow Green Blue Orange Frequency 8 4 10 4 11 11 Over the long
run, what is the probability that the first M&M you select...

Suppose that the makers of M&M's claim that 24%
of their Milk Chocolate M&M's are blue.
1) Would you expect using bags of Milk Chocolate M&M's
labeled as "Large" size, which contain more candies than the
"Medium" size bags, to result in a larger or
smaller standard error?
2) For which sample sizes (Fun-Size with 20, Vending Machine
with 55, or Medium with 415) would the Central Limit Theorem
apply?

Upon request, the Mars Company (the maker of M&M's) will
provide the color distribution for their candies. As of August
2009, they noted that
"Our color blends were selected by conducting consumer
preference tests, which indicate the assortment of
colors
that pleased the greatest number of people and created the most
attractive overall effect.
On average, our mix of colors for M&M'S CHOCOLATE CANDIES
is:
M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green,
14% bright yellow, 13% red,...

The proportion of brown M&M’s in a milk chocolate packet is
approximately 14% (Madison, 2013). Suppose a package of M&M’s
typically contains 52 M&M’s.
State the random variable.
Argue that this is a binomial experiment
Find the probability that
Six M&M’s are brown.
Twenty-five M&M’s are brown.
All of the M&M’s are brown.
Would it be unusual for a package to have only brown M&M’s?
If this were to happen, what would you think is the reason?

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 9. You
suspect that the maker's claim is not true.
Observed Counts by Color...

M&M's Color Distribution: Suppose the
makers of M&M candies give the following average percentages
for the mix of colors in their bags of plain chocolate
M&M's.
Stated Distribution of Colors
Brown
Yellow
Red
Orange
Green
Blue
Percent
30%
20%
20%
10%
10%
10%
Now, you randomly select 200 M&M's and get the counts given
in the table below. You expected about 20 blues but only got 10.
You suspect that the maker's claim is not true.
Observed...

The proportion of brown M&M’s in a milk chocolate packet is
approximately 14% (Madison, 2013). Suppose a package of M&M’s
typically contains 52 M&M’s. a.) State the random variable. b.)
Argue that this is a binomial experiment Find the probability that
c.) Six M&M’s are brown. Twenty-Five M&M’s are brown. e.)
All of the M&M’s are brown. f.) Would it be unusual for a
package to have only brown M&M’s? If this were to happen, what
would you think is...

Several years ago, the Mars, Incorporated website reported the
following percentages of the various colors of its M&M'S
candies for the "milk chocolate" variety.†
A graphical display lists 6 colors. Beside each color is a
picture of an M&M with the percentage listed below the picture.
The colors and percentages are as follows.
Brown: 13%
Yellow: 14%
Red: 13%
Blue: 24%
Orange: 20%
Green: 16%
A 14-ounce bag of milk chocolate M&M'S is randomly selected
and contains 72 brown, 74...

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