Question

Suppose it is known that 20% of college students work full time.

Part A: If we randomly select 12 college students, what is the probability that exactly 3 of the 12 work full time? Round your answer to 4 decimal places.

Answer 1

0.2369

Explanation:

To find the probability of exactly 3 out of 12 randomly selected college students working full time, we can use the binomial probability formula.

The formula for the probability of exactly k successes in n trials, where the probability of success is p, is:

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

In this case, n = 12 (number of trials), k = 3 (number of successes), and p = 0.20 (probability of success, i.e., percentage of college students working full time).

Plugging in the values:

P(X = 3) = (12 choose 3) * 0.20^3 * (1 - 0.20)^(12 - 3)

Calculating the expression:

P(X = 3) = (12! / (3! * (12 - 3)!)) * 0.20^3 * (0.80^9)

= (12! / (3! * 9!)) * 0.008 * 0.134217728

≈ 0.2369 (rounded to 4 decimal places)

Therefore, the probability that exactly 3 out of the 12 randomly selected college students work full time is approximately 0.2369.

Hope this helps!