Question

a researcher wishes to conduct a study of the color preferences of new car buyers. suppose that 30% of this population prefers the color blue. if 14 buyers are randomly selected, what is the probability that exactly 9 buyers would prefer blue?

Answer 1

To calculate the probability that exactly 9 out of 14 buyers would prefer blue, we use the binomial probability formula.

Step-by-step explanation:

To calculate the probability that exactly 9 buyers would prefer blue out of 14 randomly selected buyers, we use the binomial probability formula:

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
• n is the total number of trials (number of buyers selected)
• k is the number of successful outcomes (number of buyers who prefer blue)
• p is the probability of a successful outcome (probability of a buyer preferring blue)

In this case, n = 14, k = 9, and p = 0.3. Plugging in these values into the formula, we get:

P(X=9) = C(14, 9) * 0.3^9 * (1-0.3)^(14-9)

Simplifying this expression, we find that the probability of exactly 9 buyers preferring blue out of 14 randomly selected buyers is approximately 0.1118, or 11.18%.