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 red. If 12 buyers are randomly selected, what is the probability that exactly 2 buyers would prefer red? Round your answer to four decimal places.

Answer 1

To calculate the probability that exactly 2 buyers prefer red out of a randomly selected group of 12 buyers, we can use the binomial probability formula. The formula is P(X=k) = C(n, k) * p^k * (1-p)^(n-k). Plugging in the values, we get a probability of approximately 0.2134.

Step-by-step explanation:

To calculate the probability that exactly 2 buyers prefer red out of a randomly selected group of 12 buyers, we can use the binomial probability formula. The formula is:

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

Where:

P(X=k) is the probability of getting exactly k successes

C(n, k) is the number of combinations of n items taken k at a time

p is the probability of success (percentage of buyers who prefer red)

n is the number of trials (number of buyers selected)

In this case, p = 0.5 (50% preference for red) and n = 12 (number of buyers selected).

So, the probability of exactly 2 buyers preferring red is:

P(X=2) = C(12, 2) * (0.5)^2 * (1-0.5)^(12-2)

Using the combin( ) function on a calculator, we find that C(12, 2) = 66. plugging in the values, we get:

P(X=2) = 66 * 0.5^2 * 0.5^10 = 0.2134

Therefore, the probability that exactly 2 buyers would prefer red is approximately 0.2134