Question

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, this follows the bimodal distribution No, the trials are not independent Yes, there are 10 independent trials, each with two possible outcomes, and a constant probability associated with each possible outcome (6) 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 your decimal places) (e) What is the probability that at least 1 out of 5 randomly sampled 18-20 year olds have consumed alcoholic poverage beverages?_ please round to fois de mal places) slegte round to four decimal places) beverages

Answer 1

Given that P=0.697 (a) Answer: option (4) & Yes (6) using binomial distribution P(x): "O p q n-3 P(x=6): 10 (0.697)C1=0.694)'0-6 = 0.20294879513 :. [P(x=6): 0.2029 | co P(x =4) 10 (0.697)" (1-0.694) - 0.038 35 360385 . .:(P(x=4): 0.0384 | (d) P(x52)= P(x=0) + PCX ED +P(x-2) :51 (0.697) 0.3035+ (0.695) 6.303) as (0.697)” (0.303)3 - 0.16707160932 . P(x - 2): 0.61 | | ce) P(x>1): 1- [P(x =0)] IF(0.69+) (0.303) 1-50.00255395442] - 0.99744604558 PCY = 0.9974