Question

Mars, Inc. states that 24% of its M&M plain candies are blue and that 16% are green. Assume that they are correct and a large random sample of plain M&Ms is randomly selected from the factory.

A. What is the probability that if twenty M&Ms were eaten randomly from the sample, that exactly four of them would be green?

B. Find the mean and standard deviation for the above binomial probability distribution in part c. Based on that, would it be unusual that exactly four would be green from a random selection of twenty M&Ms? Why or why not?

Answer 1

Mars, Inc. states that 24% of its M&M plain candies are blue and that 16% are green. Assume that they are correct and a large random sample of plain M&Ms is randomly selected from the factory.

Let define a random variable X that represent number of green candies.

(A) What is the probability that if twenty M&Ms were eaten randomly from the sample, that exactly four of them would be green?

Solution::

Here we eaten 20 M&Ms candies.

The random variable X follow binomial distribution with parameters n=20 and p=0.16

The p.m.f of X is given by

We need to find P(X=4)

B. Find the mean and standard deviation for the above binomial probability distribution.

Solution::

The mean is given by

The standard deviation is given by

(C)Based on that, would it be unusual that exactly four would be green from a random selection of twenty M&Ms? Why or why not?

Solution::

The usual range is given by

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This is not unusual, because 4 green belongs to the usual range.