Question

Suppose that historically, 33% of applicants that are offered admittance to Georgia Southern actually enroll, while the others take offers somewhere else. If Georgia Southern will accept 11700 this coming year, what is the probability that less than 3000 will actually enroll?

Calculate n*p and n*(1-p) and check that each is greater than 10. Does this situation meet the condition for approximating a binomial with a normal?

Answer 1

Here p=0.33 and n=11700

So np=11700*0.33=3861>10 and n(1-p)=11700*0.67=7839>10

So conditions for normal approximation is satisfied

Hence we can use normal approximation to find required probability

And standard deviation is

Now we need to find

As we can use normal approximation we can convert x to z