Question

Grab your bag of M & Ms and sort them out by color. Record the number of each color in row A of the table below. Also record the total number of M&Ms in your bag, n.

Calculate the expected value of each color in a bag of size n. Record your results in Row B.

Calculate the standard deviation for each color in a bag of size n. Record your results in Row C.

Using the Range-Rule-Of-Thumb, calculate the maximum usual value and the minimum usual value for a

bag of size n. Record your results in Row D.

Are the color counts from your bag of M & Ms considered usual or unusual based on the Range-Rule-Of-

Thumb? Record your results in row E.

Answer each of the questions below on a separate sheet of paper.

*The population color distribution below is claimed by the M & Ms corporation.

The distribution that M & Ms claims can be thought of as a binomial distribution for each color choice. Thus, “success”=claimed color and “failure”=not claimed color (any other color). Assume the distribution claimed by M&Ms is true:

n=

Actual
Cou**nt**

**Red
1**

**Blue
9**

**Green
14**

**Yellow
10**

**Brown
10**

**Orange
11**

***Claimed
Distribution p**

**13%
Red**

**24%
Blue**

**16%
Green**

**14%
Yellow**

**13%
Brown**

**20%
Orange**

A

Actual Count

B

Expected Value

C

Standard Deviation

D

Max

Min

E

Usual or unusual?

Binomial Distribution Questions using the Claimed M&Ms Distribution

(use the claimed p values from row *, n is the number of M&Ms in your bag and x is the value from row A)

1. What is the
probability of selecting the same number of BLUE M&Ms as you
counted in your bag?

2. What is the probability of selecting the same number of RED
M&Ms as you counted in your bag?

3. What is the probability of selecting the same number of ORANGE
M&Ms as you counted in your bag?

Probability Questions using Your Sample Data

(n is the number of M&Ms in your bag and x is the value from row A)

Using your sample of n M&Ms as a probability experiment, what is the probability of

selecting a green M&M from your bag?

You reach into your bag, pull out a green M&M and eat it; what is the probability that you

will choose a green M&M again?

What is the probability of selecting two blue M&Ms from your bag? (without replacement)

Answer #1

A fun size bag of M&Ms has 4 blue, 3 orange, 3 red, 2
green, 2 yellow, and 1 brown M&Ms. What is the probability of
randomly selecting 5 M&Ms where 3 are blue and 2 are red?

1- A single serving of milk chocolate M&M candies is 50
pieces. In a standard bag of M&Ms there are six colors (brown,
yellow, green, red, orange, and blue) and assume equal
probabilities for the color of a randomly selected M&M.
a) What is the mean value for the number of red M&Ms in a
single serving of randomly selected M&Ms?
b)What is the variance of the number of red M&Ms in a single
serving?
c) What is the probability...

A manufacturer of colored candies states that 13% of the
candies in a bag should be brown, 14% yellow, 13% red, 24%
blue, 20% orange, and 16% green. A student randomly selected a
bag of colored candies. He counted the number of candies of each
color and obtained the results shown in the table. Test whether the
bag of colored candies follows the distribution stated above at the
a=0.05 level of significance.
Color
Brown
Yellow
Red
Blue
Orange
Green
Frequency...

M&Ms are multicolored candies in a bag with six colors:
Brown, Blue, Red, Yellow, Green and Orange. Mars now claims that
all six colors are equally likely. In an attempt to reject the
claim, an 8-oz bag of M&Ms was purchased and the colors
counted. The results of the count are below. Does this sample
contradict Mars’ claim when α = 0.10? Brown Blue Red Yellow Green
Orange 37 41 32 25 36 39 If the claim is true what...

Mars Inc. claims that they produce M&Ms with the following
distributions:
Brown
30%
Red
20%
Yellow
20%
Orange
10%
Green
10%
Blue
10%
A bag of M&Ms was randomly selected from the grocery store
shelf, and the color counts were:
Brown
23
Red
23
Yellow
20
Orange
15
Green
17
Blue
15
Using the χ2 goodness of fit test to determine if the
proportion of M&Ms is what is claimed, what is the test
statistic?
a) χ2 = 10.409
b)...

A snack-size bag of M&Ms candies is opened. Inside, there
are 12 red candies, 12 blue, 7 green, 13 brown, 3 orange, and 10
yellow. Three candies are pulled from the bag in succession,
without replacement. What is the probability that the first two
candies drawn are blue and the third is green?

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...

Mars Inc. claims that they produce M&Ms with the following
distributions:
Brown
30%
Red
20%
Yellow
20%
Orange
10%
Green
10%
Blue
10%
A bag of M&Ms was randomly selected from the grocery store
shelf, and the color counts were:
Brown
25
Red
23
Yellow
21
Orange
13
Green
15
Blue
14
Using the χ2 goodness of fit test (α = 0.10) to
determine if the proportion of M&Ms is what is claimed. Select
the [p-value, Decision to Reject (RH0)...

Use the distribution below to test that Plain M&Ms follow
the stated distribution. Discuss your choice of ?. Would a
different ? have changed your conclusion?
M&M states the following distribution for Plain M&Ms:
Red = 13%, Orange = 20%, Yellow = 13%, Green = 20%, Blue = 20%,
Brown = 14%
Total amount of Plain M&Ms: 678
Red=69 Orange=216 Yellow=75 Green=61 Blue=187 Brown=70

7. Table #4.1.2 contains the number of M&M’s of each
color that were found in a case (Madison, 2013).
Table #4.1.2: M&M Distribution
Blue
Brown
Green
Orange
Red
Yellow
Total
481
371
483
544
372
369
2620
Find the probability of choosing each color based on
this experiment

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