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.