3.27 Underage drinking, Part II: We learned in Exercise 3.25 that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 year olds. (a) How many people would you expect to have consumed alcoholic beverages? (round to one decimal place) What is the standard deviation? (round to two decimal places) (b) Would you be surprised if there were 45 or more people who have consumed alcoholic beverages? No, 45 or more accounts for six different events -- this wouldn't be surprising Yes, 45 is more than two standard deviations above the expected value (mean) No, it is just as likely as any other outcome Yes, 45 out of 50 is 90% (c) What is the probability that 45 or more people in this sample have consumed alcoholic beverages?
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!
3.27 Underage drinking, Part II: We learned in Exercise 3.25 that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 year olds.
(a) How many people would you expect to have consumed alcoholic beverages? (round to one decimal place)
What is the standard deviation? (round to two decimal places)
(b) Would you be surprised if there were 45 or more people who have consumed alcoholic beverages?
- No, 45 or more accounts for six different
events -- this wouldn't be surprising
- Yes, 45 is more than two standard deviations above the
expected value (mean)
- No, it is just as likely as any other outcome
- Yes, 45 out of 50 is 90%
(c) What is the
(round to four decimal places)
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