Sangeetha Pulapaka

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.

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

Our sample size n = 60, and p = 0.56

Expected successes = np = 33.6 > 10

Expected failures = n(1-p) = 60 ( 1- 0.56) = 33.6 > 10

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

The shape of the sampling distribution of \widehat{p} is approximately normal.