Question 1: (Marks: 5+3=8)
(a) The mean height of soldiers is 69.33 inches with a variance of 11.8. Assuming the distribution of heights to be normal, how many soldiers in a regiment of 1000 would you expect to be at least 6 feet tall?
(b) In a hypergeometric distribution, n = 4, k = 4 and N = 10. Calculate the mean and Standard deviation of hypergeometric distribution.
Question 2: (Marks: 5+2=7)
(a) A population consists of 5 values 1, 3, 5, 7, 9. Take all possible samples of size 2 which can be drawn without replacement from this population. Make the sampling distribution of sample means.
(b) Random samples each of size 50 are drawn from two normal populations X and Y with means = 120, = 100 and variances = 10, = 20. Find the mean and variance for the sampling distribution of.
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