Let X have a Bernoulli distribution with pmf

We would like to test the null hypothesis H0: p ‰¤ 0.4 against the alternative hypothesis H1: p > 0.4. For the test statistic, use

is a random sample of size n from this Bernoulli distribution. Let the critical region be of the form C = {y: y ‰¥ c}.
(a) Let n = 100. On the same set of axes, sketch the graphs of the power functions corresponding to the three critical regions, C1 = {y : y ‰¥ 40}, C2 = {y : y ‰¥ 50}, and C3 = {y : y ‰¥ 60}. Use the normal approximation to compute the probabilities.
(b) Let C = {y : y ‰¥ 0.45n}. On the same set of axes, sketch the graphs of the power functions corresponding to the three samples of sizes 10, 100, and 1000.

f(xp) = pr(1-p)1-x , x=0, 1, 0-p 1. Y 1 X, where X1, X2.. ,X