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 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? O No, the normal distribution should be used No, this follows the bimodal distribution O Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome O No, the trials are not independent (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)
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 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? O No, the normal distribution should be used No, this follows the bimodal distribution O Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome O No, the trials are not independent (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)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Concept explainers
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
Transcribed Image Text: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 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?
O No, the normal distribution should be used
O No, this follows the bimodal distribution
Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant
probability associated with each possible outcome
O No, the trials are not independent
(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)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON