The results of the 2009 Survey on Drug Use and Health found that among young adults ages 18-25, in the last month, 22.8% had used marijuana; 2.4% had used cocaine; 3.8% had abused prescription drugs. If we select 500 young adults at random, approximate the probability of the given event.
a. Less than 10 had abused prescription drugs
b. Between 80 and 100 had used marijuana
c. More than 5 had used cocaine.
Here is my explanation:
a. This is a binomial probability. since np=500*3.8%=19>5, n*(1-p)=500*(1-3.8%)=481>5, we could use normal distribution to approximate the probability.
The solution solves a statistics problem regarding young adult drug use.