A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 40% of this population prefers the color green. If 12 buyers are randomly selected, what is the probability that exactly 10 buyers would prefer green?

The probability that exactly 10 buyers would prefer green is 0.0025.

Step-by-step explanation:

Let the random variable X be defined as the number of buyers who would prefer green.

The probability of a buyer preferring Green is, P (X) = p = 0.40.

The sample of buyers selected is of size n = 12.

The color preference of the buyers are independent of each other.

The random variable X satisfies all the conditions of a Binomial distribution.

Thus,

The probability function of a Binomial distribution is:

Compute the probability that exactly 10 buyers would prefer green as follows:

Thus, the probability that exactly 10 buyers would prefer green is 0.0025.