In a particular faculty 60% of students are men - 94822

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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.
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(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

(b) P