According to the National Center for Health Statistics, 15% of all Americans have hearing trouble. (a) In

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According to the National Center for Health Statistics, 15% of all Americans have hearing trouble.

(a) In a random sample of 120 Americans, what is the probability at most 12% have hearing trouble?

(b) Suppose that a random sample of 120 Americans who regularly listen to music using headphones results in 26 having hearing trouble. What might you conclude?

Approach First, determine whether the sampling distribution is approximately normal by verifying that the sample size is less than 5% of the population size and that np(1 –p) ≥ 10. Then use the normal distribution to determine the probabilities.

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