3.25 Underage drinking, Part I:Data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests that 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. (a) Suppose a random sample of the ten 18-20 year olds is taken. Is the use of the binomial distribution appropriate for calculating the probability that exactly six consumed alcoholic beverages?

• No, the normal distribution should be used
• No, the trials are not independent
• Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome
• No, this follows the bimodal distribution

(b) Calculate the probability that exactly 6 out of 10 randomly sampled 18- 20 year olds consumed an alcoholic drink.

(please round to four decimal places)

(c) What is the probability that exactly four out of the ten 18-20 year olds have not consumed an alcoholic beverage?(please round to four decimal places)

(d) What is the probability that at most 2 out of 5 randomly sampled 18-20 year olds have consumed alcoholic beverages?

(please round to four decimal places)

(e) What is the probability that at least 1 out of 5 randomly sampled 18-20 year olds have consumed alcoholic beverages?

(please round to four decimal places)

Please provide formula