Question

1. In a particular facility, 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.

1. What is the expected value and variance of the random variable X? (6 points)
   
   
   
2. In a random sample of 50 students what is the probability that more than half are women?
   Calculate the exact binomial probability. (6 points)
   
   

3. Are the conditions that permit you to use a normal approximation to the binomial satisfied? Explain (6 points)

4. Recalculate the probability in part b using a normal approximation without the continuity correction. (6 points)

5. Recalculate the probability in part b using a normal approximation with the continuity correction. (6 points)

Answer 1

56.26 (0.40) (o 6o So So-So 5 o : 0.05 343チ appooximaion e binoO noi 0.0 4.9 25) : 112 : .05Sq