The proportion of all US adults who eat popcorn when they go to the movie theater is p is equal to 0 point 8 7 A random sample of 20 US adults was selected and asked if they eat popcorn when they go to the movie theater. Which of the following is the shape of the sampling distribution of hat p ?

For the sampling distribution of the sample proportion, the success-failure condition requires both np and n(1 − p) to be at least 10. Here, n(1 − p) = 20(1 − 0.87) = 2.6, so the distribution is not approximately Normal. Since p = 0.87 is close to 1, sample proportions tend to be near the high end, with a tail toward lower values; the distribution is skewed to the left. Choice C describes this shape.

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