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According to the statistics of a famous high school in Canada, all their graduates went to either A or B for university study. Following are the proportions of graduates who went to the two universities.

University Proportion
A 1-k
B k

Suppose k = 0.4
(a) What is the standard deviation of the number of graduates going to B from random samples of the graduates, each with sample size 50?

(b) What is the probability that more than half of graduates going to A in a random sample of 8 graduates?

(c) What is the chance of having at least one graduate going to B and at least one graduate going to A in a random sample of 10 graduates?

(d) Based on the most updated annual report from the school, there were 1280 graduates last year and 690 of them went to A. What is the estimated value of k?

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