Question

In a study about car color preferences, assume 40% of the population prefers the color green. If 20 buyers are randomly selected, what is the probability that at least 10 of them prefer green?

Answer 1

To find the probability that at least 10 out of 20 buyers prefer the color green, we can use the binomial probability formula. The probability of success (buyers preferring green) is 0.4, and the number of trials is 20. We need to find the sum of the probabilities for 10 or more successes.

Step-by-step explanation:

To find the probability that at least 10 out of 20 buyers prefer the color green, we can use the binomial probability formula. The probability of success (buyers preferring green) is 0.4, and the number of trials is 20. We need to find the sum of the probabilities for 10 or more successes, which includes 10, 11, 12, ..., 20. To calculate this, we can use a binomial calculator or a cumulative binomial probability table.

The probability of getting exactly k successes (where k ranges from 10 to 20) out of n trials is given by the formula:

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

where P(X=k) is the probability of getting k successes, n is the number of trials, p is the probability of success, and C(n, k) is the number of combinations of n items taken k at a time, given by the formula:

C(n, k) = n! / (k!(n-k)!)

Using this formula, we can calculate the probabilities for each value of k and then sum them up to find the probability of at least 10 successes.