The student body of a large university consists of 60% 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?
A) 0.1064
B) 0.0896
C) 0.0168
D) 0.8936

Question

Quizplus · Accepted Answer

The probability of selecting a female student is 0.6. The probability of selecting a male student is 0.4. The probability of selecting at least 7 female students out of 8 is given by the binomial distribution:P(X >= 7) = 1 - P(X < 7) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6))Using the binomial distribution formula, we can calculate each term:P(X = 0) = (8 choose 0) * (0.6)^0 * (0.4)^8 = 0.000064P(X = 1) = (8 choose 1) * (0.6)^1 * (0.4)^7 = 0.000448P(X = 2) = (8 choose 2) * (0.6)^2 * (0.4)^6 = 0.002048P(X = 3) = (8 choose 3) * (0.6)^3 * (0.4)^5 = 0.007168P(X = 4) = (8 choose 4) * (0.6)^4 * (0.4)^4 = 0.02048P(X = 5) = (8 choose 5) * (0.6)^5 * (0.4)^3 = 0.049152P(X = 6) = (8 choose 6) * (0.6)^6 * (0.4)^2 = 0.0896Therefore, P(X >= 7) = 1 - (0.000064 + 0.000448 + 0.002048 + 0.007168 + 0.02048 + 0.049152 + 0.0896) = 0.1064.

The Student Body of a Large University Consists of 60