In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students what is the probability that more than half are women?
Let the random variable X = number of women in the sample.
Assume X has the binomial distribution with n = 50 and p = 0.4.
a. What is the expected value and variance of the random variable X?
b. Calculate the exact binomial probability.
c. Are the conditions that permit you to use a normal approximation to the binomial satisfied? Explain
d. Recalculate the probability in part b using a normal approximation without the continuity correction.
e. Recalculate the probability in part b using a normal approximation with the continuity correction.
(a) n = 50, p = 0.4, q = 1 – p = 0.6
Expected value = np = 50 * 0.40 = 20
Variance = npq = 50 * 0.4 * 0.6 = 12