Samples of size n produced sample proportions pˆ as shown. In each case decide whether or not the sample size is large enough to assume that the sample proportion Pˆ is normally distributed.
n = 30, pˆ=0.72
n = 30, pˆ=0.84
n = 75, pˆ=0.84

Question

Samples of size n produced sample proportions pˆ as shown. In each case decide whether or not the sample size is large enough to assume that the sample proportion Pˆ is normally distributed.
n = 30, pˆ=0.72
n = 30, pˆ=0.84
n = 75, pˆ=0.84

kropot72 · Answer

In each case the sample size is equal to, or greater than, 30. Also the sample proportion in each case is much greater than zero. Therefore the Normal Approximation to the Binomial can be used.