Question

The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female?

a. 0.0007
b. 0.2936
c. 0.0413
d. 0.0896

Answer 1

The probability that exactly two out of eight randomly chosen students are female is approximately 0.26844.

Step-by-step explanation:

To find the probability that exactly two out of eight randomly selected students are female when 60% of the university's student body is female, we can use the binomial probability formula:

P(X=k) = C(n, k) * p^k * q^(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 (60% or 0.6),

q is the probability of failure (40% or 0.4),

n is the number of trials (8),

k is the number of successful outcomes we want (2).

Plugging the given values into the formula, we have:

P(X=2) = C(8, 2) * (0.6)^2 * (0.4)^(8-2).

Simplifying the calculation, we get:

P(X=2) = 28 * 0.36 * 0.262144 = 0.26844.

Therefore, the probability that exactly two of the eight randomly selected students are female is approximately 0.26844.