Underage drinking Part II We learned in Exercise 325 that ab

Underage drinking, Part II. We learned in Exercise 3.25 that about 70% 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? And with what standard deviation?

(b) Would you be surprised if there were 45 or more people who have consumed alcoholic bever- ages?

(c) What is the probability that 45 or more people in this sample have consumed alcoholic bev- erages? How does this probability relate to your answer to part (b)?

Solution

Normal Distribution
a)
Mean ( np ) =35
Standard Deviation ( npq )= 50*0.7*0.3 = 3.2404
Normal Distribution = Z= X- u / sd                   
b)
P(X < 45) = (45-35)/3.2404
= 10/3.2404= 3.086
= P ( Z <3.086) From Standard NOrmal Table
= 0.999                  
P(X >= 45) = 1 - 0.999 = 0.001
Yes, because the probability of such occurence is highly immpossible
c)
It is 0.001