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.