Answer to Question #292295 in Statistics and Probability for Yaku

Question

5. Random samples of size n were selected from binomial populations with population parameters p given here. Find the mean and the standard deviation of the sampling distribution of the sample proportion

^p = X \bar

in each case:

a) n = 100, p = 0.3;

b) n = 400, p = 0.1;

c) n = 250, p = 0.6.

6. a) Let T have a t-distribution with 10 degrees of freedom. Find P(T \legslant  1.812).
b) If F has an F-distribution with 5 and 10 degrees of freedom. find a and b, such that P(a \legslant F \legslant b) = 0.9.

c) Let Z be a standard normal random variable, independent of Y which is chi-square random variable with 4 degrees of freedom. Find the value of a so that P(|Z| \legslant a \sqrt{Y} )=   0.9.

d) If X ~ X²₅, determine the constants c and d such that P(c < X <d) = 0.95 and P(X < c) = 0.025.

e) Let X ~ N(5, 10). Find P(0.04 < (X - 5)² < 38.4).