On Jun 11, 12:27 pm, tutorny <tuto...@gmail.com> wrote: > I am looking at solving the following problem: > > Past records show that at a given college 20% of the students who > began as psychology majors either changed their major or dropped out > the school. An incoming class has 110 > beginning psychology majors. What is the probability that as many as > 30 of these students leave the psychology program? > > I think that I can solve it using the normal approximation to the > binomial probability distribution, as follows: > > n =110, p = 0.20 > mean = u = np = 110*0.20 = 22 > standard deviation = s.d. = (n*p*q)^.5 = (110*.20*.80)^.5 = 4.1952 > > We want P(x <=30) > > When x = 30, z = (x - u)/s.d = (30 - 22)/4.1952 = 1.9069 > > So, we want P(z<=1.9069) = 0.9717 > > So, the answer is 97.17 percent. > > Can you tell me if you see anything wrong with this answer, or the way > that I solved this problem? Any help is greatly appreciated.
Mainly that you answered the wrong question.
You are told that on average 20% drop out. So a 20% drop out rate is most likely. A rate of 15% or 25% would be less likely. A rate of 10% or 30% even less likely.
Do you really think there is a 97% chance that there will be a 30% drop out rate? Suppose I asked you the probability that 100 of the students would drop out. How would you calculate that? Do you think that is a higher probability than only 30 students dropping out?