Question

After hearing a national result that 27% of students had engaged in binge drinking (5 drinks at a sitting for men, 4 for women) in the past month, a professor surveyed a random sample of 100 students at his college and asked about their drinking habits in the past month.

• What are the values for n and p in this question?
• What is the probability that 20 or fewer students engaged in binge drinking in the past month?
• Is this result surprising? Explain.
• Without doing the actual calculation, should this answer to this question be greater than or less than or the same as the answer to Question 1? Explain your thinking.

Answer 1

Here, n = sample size = 100 and p = success probability = 27% = 0.27.
Prob.(20 or fewer students engaged in binge drinking in the past month) = P(X <= 20) = 0.0684.
Yes, the result is surprising because the above-mentioned probability is very low.

The answer to this question will be less than the answer to Question 1, because we are using CLT in our calculations, which is approximating the probability.