Sahil Khan
0

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.