Data collected by the Substance Abuse and Mental Health Services Administration suggest that 69.7% of 18-20 year olds consumed alcoholic beverages in any given year. Suppose we have a simple random sample of ten 18-20 year olds. Let's use a Binomial Distribution to describe the number of individuals in this sample that have consumed an alcoholic beverage. Let X represent our random variable, the number of individuals in this sample that have consumed an alcoholic beverage. For each individual we can record one of two outcomes, 0=has not consumed alcohol or 1=has consumed alcohol. Since we have 10 independent individuals and the probability that each one has consumed alcohol is the same, we can use a Binomial distribution to model our random variable X. The Binomial distribution requires two parameters: n=the number of trials p=probability of "success" Note "success" is in quotes because there is not necessarily a positive connotation associated with the outcome that is a success. For this example, the number of trials is 10 (since there are 10 individuals) and the probability that each individual has consumed alcohol is 0.697.n = 10 p = 0.697 Let's find the probability that exactly 5 of the individuals in the sample have consumed alcohol. We can do this using the probability mass function ofa Binomial distribution (page 150). P(X = w) = (2)10\"1 -p)\"'\"\"" We've already defined n and p. In the case where we want to calculate the probability that exactly 5 individuals in the sample have consumed alcohol, a: = 5. Plug in n, p, and a: into the probability mass function above. P(X = 5) = (150)0.6975(1 0.697)10'5 Q5 0 Homework 0 Unanswered Evaluate the expression above to nd the probability that exactly 5 ofthe ten individuals in the sample have consumed alcohol. Round your answer to three decimal places. Type your numeric answer and submit % 06 Homework . Unanswered Now try calculating the probability that exactly 2 of the 10 individuals have consumed alcohol. Round your answer to three decimal places. Type your numeric answer and submit