> 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. > > Thanks! >
Let's start off with the professor's interpretation of the problem which is that we are trying to evaluate Prob(X <= 30). Are you allowed to use the binomial distribution to obtain the calculation exactly?
If X is binomial with p = 0.20 and N = 110, then Prob(X <= 30) = 0.9753, which is slightly greater than your normal approximation.