Answer:
the probability that the graduate program will have enough funding for all student that join the program is 0.3653 (36.53%)
Step-by-step explanation:
since each student is independent on others the random variable X= x students of 45 applicants will join the program has a binomial probability distribution
P(X=x)= n!/[(n-x)!*x!]*p^x*(1-p)^x
where
n= total number of students= 45
p= probability that a student join the program= 0.7
x= number of students that join the program
then in order to have enough funding x should not surpass 30 students , then
P(X≤30)= ∑P(X) for x from 1 to 30 = F(30)
where F(30) is the cumulative probability distribution
then from binomial probability tables
P(X≤30)= F(30)= 0.3653 (36.53%)
therefore the probability that the graduate program will have enough funding for all student that join the program is 0.3653 (36.53%)
