Question

Suppose the event of a student’s application to a university being accepted follows the binomial probability and the successful rate is 80%. Please finish the following tasks? (1) Determine the expected number of acceptances for the next 7 applicants and the standard deviation. (2) What is the probability that among the next 9 applicants exactly 5 will be accepted?

Answer 1

X : Number of student’s application to a university being accepted

p: Probability that a student's application to a university being accepted = 80/100 =0.8

q =1 - p = 1-0.8 = 0.2

(1) Determine the expected number of acceptances for the next 7 applicants and the standard deviation

For this scenario , n= 7

Therefore X follows binomial distribution with n=7 and p=0.8

Expected number of acceptances = E(X) = np = 7 x 0.8 = 5.6

Expected number of acceptances for the next 7 applicants = 5.6

Standard deviation =

Standard deviation = 1.058300524
(2)

Probability that among the next 9 applicants exactly 5 will be accepted

For this scenario , n= 9,

Therefore X follows binomial distribution with n=7 and p=0.8

And the probability mass function of x : Probability that 'r' applicants will be accepted

Probability that among the next 9 applicants exactly 5 will be accepted = P(X=5)

Probability that among the next 9 applicants exactly 5 will be accepted = 0.066060288