Question

According to a study by the National Institute on Alcohol Abuse and Alcoholism, 19% of college students between the ages of 18 and 24 meet the criteria for alcohol abuse or dependence.

Coker University wants to determine whether it has a lower, average, or higher rate of alcohol abuse than the national average. A random sample of 49 students is selected, and evaluated for signs of alcohol abuse or dependence.

a. Identify n for the binomial experiment.

b. Identify p for the binomial experiment.

c. Find the probability that 4 or fewer of the students in the sample exhibit signs of alcohol abuse or dependence. Round your answer to 4 decimal places.

d. If 4 out of the sample of 49 exhibited signs of alcohol abuse or dependence, would Coker University be justified in claiming that an unusually low percentage of our students exhibit signs of alcohol abuse or dependence?

Select your answer from one of the following options.

• a.No, because the probability in part c. represents a usual event, meaning it is within the usual range of variation due to random sampling.
• b.No, because the probability in part c. represents an unusual event, meaning it is very unlikely Coker University would get these results.
• c.Yes, because 4/49 = 8% is lower than the national average of 19%
• d.Yes, because the probability in part c. represents an unusual event, meaning the percentage (4/49 = 8%) is unusually low compared to the national average (19%).

Answer 1

Let X denote the number of students between the ages of 18 and 24 meet the criteria for alcohol abuse or dependence.

Answer a. n = sample size = 49

Answer b. p = probability of students exhibit signs of alcohol abuse or dependence = 0.19

Answer c.

So,

Answer d. Yes, because the probability in part c. represents an unusual event, meaning the percentage (4/49 = 8%) is unusually low compared to the national average (19%).