Are 14% of M&M Candies Yellow? Mars, Inc. claims that 14% of its M&M plain candies are yellow, and a sample of 100 such candies is randomly selected.

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

b. Data Set 20 in Appendix В consists of a random sample of 100 M&Ms, including 8 that are yellow. Is this result unusually low? Does it seem that the claimed rate of 14% is wrong?

Answer:

Step 1:

Given that, Mars, Inc. claims that 14% of its M&M plain candies are yellow, and a sample of 100 such candies is randomly selected.

Here, n = 100,p = 14% = 0.14, q = 1- p = 1- 0.14 = 0.86.

a). The mean and standard deviation for the number of yellow 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 = 1000.14 = 14.

Variance = npq = 100(0.14)(0.86) = 12.04.

And standard deviation = = =