Question

The student body of a large university consists of 65% female students. A random sample of 8 students is selected. What is the probability that among the students in the sample at least 7 are female?

Answer 1

Answer:

16.9%

Step-by-step explanation:

If at least 7 are female, that means either 7 or 8 are female.

Use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

Here, n = 8, p = 0.65, and r = 7 or 8.

P = ₈C₇ (0.65)⁷ (0.35)⁸⁻⁷ + ₈C₈ (0.65)⁸ (0.35)⁸⁻⁸

P = (8) (0.65)⁷ (0.35)¹ + (1) (0.65)⁸ (0.35)⁰

P = 8 (0.65)⁷ (0.35) + (0.65)⁸

P = 0.169