Question

LSU students can be In-state and out of state. A recent survey shows that 80% students of LSU are In-state.

1. If you pick 100 LSU students what is the probability that at least 80 of them will be In-state students.

2. If you pick 100 LSU students what is the probability that at least 80 of them will be out of state students.

Answer 1

Let p be the proportion of lsu students who are instate. So we have p= 0.8

Now, n=100, so np=80, np(1-p) = 16

Let X be the number of students of out 100 who are instate, so

P(X>=80) = P(Z>= 80-80/√16) = P(Z>0) = 1- P(Z<0) = 0.5

2. Let q be the proportion of lsu students who are out state. So q=0.2

So nq= 20, nq(1-q) = 16

Let Y be the number of outstate students out of 100,

So P(Y>=80) = P(Z>= 80-20/√16) = P(Z>=15) = 1- P(Z<=15) < 0.000001

So we can say it is 0.