Sahil Khan

We are looking at which conditions does the sampling distributions of the sample proportions, looks, skewed to the left, skewed to the right, approximately normal, or uniform.

Our sample size n = 70  and p = 0.2

Expected successes:  np = 70(0.2) = 14

Expected failures ; n(1-p) = 70( 1 - 0.2) = 70(0.8) = 56

We know that when we have,  np≥10, and  n(1−p)≥10, and both of these are true, proportions of sample distributions, will be approximately normal in shape.

We have a normal sampling distribution because we expect at least 10 successes and 10 failures per sample.

So, the shape of the sampling distribution of \widehat{p}​ is approximately normal.