In a particular faculty 60% of students are men and 40% are women

n 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.