according to a gallup poll in 2006 about 10 percent of americans said - According to a Gallup poll in 2010 about 20 percent of Americans said they were very afraid of flying on an airplane suppose that we took random samples of n = 70 people from this population and computed the proportion of people in each sample who were very afraid of flying. Which of the following distributions is the best approximation of the sampling distribution of the proportion of people who were very afraid of flying?

Sahil Khan (last edited 2 years ago)

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.