Are 20% of M&M Candies Orange? Mars, Inc. claims that 20% of its M&M plain candies are orange, and a sample of 100 such candies is randomly selected.

a. Find the mean and standard deviation for the number of orange candies in such groups of 100.

b. Data Set 20 in Appendix В consists of a random sample of 100 M&Ms, including 25 that are orange. Is this result unusually high? Does it seem that the claimed rate of 20% is wrong?

Answer:

Step 1:

Given that, Mars, Inc. claims that 20% of its M&M plain candies are orange, and a sample of 100 such candies is randomly selected.

Here, n = 100,p = 20% = 0.2, q = 1- p = 1- 0.2 = 0.8.

a). The mean and standard deviation for the number of orange candies in such groups of 100.

For binomial distribution the mean and variance is given by the following formula.

Here ‘x’ follows binomial distribution with sample size “n” and proportion “p”.

i.e, X

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

Mean μ = np = 1000.2 = 20.

Variance = npq = 100(0.2)(0.8) = 16.

And standard deviation = = =