Question

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 20 buyers ate randomly selected, what is the probability that exactly a fifth of the buyers would prefer green? Round your answer to four decima places.

Answer 1

To determine the probability that exactly 4 out of 20 new car buyers prefer the color green, when 40% of the population prefers green, we use the binomial probability formula. By inputting n=20, k=4, and p=0.40 into the formula, we calculate the probability of this specific outcome.

Step-by-step explanation:

The question asks about the probability of exactly 4 new car buyers out of 20 preferring the color green, given that 40% of the population prefers green. This is a binomial probability problem where the number of successes in trials (n) is fixed, each trial is independent, and the probability of success (p) is constant. In this case, n=20, the number of trials (buyers), and p=0.40, the probability of preferring green.

To find the probability of exactly 4 buyers preferring green, we use the binomial probability formula:

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

Where:

• n = 20 (total number of buyers)
• k = 4 (number of buyers who prefer green)
• p = 0.40 (probability of preferring green)

The calculation involves choosing 4 individuals from 20 and multiplying by the probability of 4 people preferring green and the remaining 16 not preferring green.