5.75 Binge drinking. The Centers for Disease Control and Prevention finds that 28% of people aged 18 to 24 years binge drank. Those who binge drank averaged 9.3 drinks per episode and 4.2 episodes per month. The study took a sample of over 18,000 people aged 18 to 24 years, so the population proportion of people who binge drank is very close to p = 0.28.²³ The administration of your college surveys an SRS of 200 students and finds that 56 binge drink.

1. (a) What is the sample proportion of students at your college who binge drink?

2. (b) If, in fact, the proportion of all students on your campus who binge drink is the same as the national 28%, what is the probability that the proportion in an SRS of 200 students is as large or larger than the result of the administration’s sample?

3. (c) A writer for the student paper says that the percent of students who binge brink is higher on your campus than nationally. Write a short letter to the editor explaining why the survey does not support this conclusion.