We are interested in the number of orange M&M’s selected from a sample of ten. U

Question

We are interested in the number of orange M&M’s selected from a sample of ten. Use the “Per M&M’s Official” column to find the probability of selecting an orange.

Let X = the number of orange M&M's selected

X ~   Binomial (n=10, p=0.20 )

Question 1

What is n? Give the numerical value.

Question 2

What is p?   Give in the form of a decimal.

Question 3

What is the average number of orange M&M’s?

Question 4

What is the standard deviation of orange M&M’s?  Give solution to three decimal places.

Question 5

Find the probability of selecting seven or more orange M&M’s out of a sample of ten.  Give solution to four decimal places.

Question 6

When sampling 10 M&M’s, what is the probability of getting exactly three that are orange?  Give solution to four decimal places.   

Question 7

What is the probability that the number of orange M&M’s drawn out of ten is more than two, but less than eight?  Give solution to four decimal places.

Question 8

Find the probability of selecting more than 3 orange M&M’s out of a sample of ten.  Give solution to four decimal places.

Question 9

BONUS: When sampling 10 M&M’s, what is the probability of getting eight that are not orange?  Give solution to four decimal places.

Explanation / Answer

This is a Binomial Distribution

a) n = 10, since number of trials are 10 or the sample size is 10

b) p = 0.2, given probability per M&M official

c) average number of orange M&M is given by = np (Mean for binomial distribution is given by np)

average number of orange M&M is given by = 10*.2 = 2

d) standard deviation of orange M&M = (np(1-p))1/2

(Standard Deviation for binomial distribution is given by np(1-p))

standard deviation of orange M&M = (10*.2*.8)1/2

standard deviation of orange M&M = (1.6)1/2

standard deviation of orange M&M = 1.265

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