Question

A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color green. If 15 buyers are randomly selected, what is the probability that exactly a third of the buyers would prefer green?

Answer 1

The probability of exactly a third of the 15 randomly selected car buyers preferring the color green is approximately 30.08%.

Step-by-step explanation:

The probability of a randomly selected new car buyer preferring the color green is 50%. To find the probability that exactly a third of the 15 buyers selected prefer green, we can use the binomial probability formula. The formula is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

In this case, n = 15 (number of buyers selected), k = 5 (one third of 15), and p = 0.5 (probability of a buyer preferring green). Plugging these values into the formula, we get:

P(X = 5) = C(15, 5) * 0.5^5 * (1-0.5)^(15-5)

Calculating this, we find that the probability is approximately 0.3008, or 30.08%.