Question

70% of the students applying to a university are accepted. Assume the requirements for a binomial experiment are satisfied for 10 applicants. a. What is the probability that among the next 10 applicants 8 or more will be accepted. b. What is the probability that among the next 10 applicants 4 or more will be accepted? (Use the binomial table for this problem) c. What is the expected number of the next 10 applicants that will be accepted?

Answer 1

X ~ B ( n = 10 , P = 0.7 )

Part a)
P(X = 8 ) = 0.2335
P(X = 9 ) = 0.1211
P(X = 10 ) = 0.0282

P ( X >= 8 ) = 0.3828

Part b)

P(X = 0 ) = 0
P(X = 1 ) = 0.0001
P(X = 2 ) = 0.0014
P(X = 3 ) = 0.009

P ( X >= 4 ) = 1 - P ( X <= 3 ) = 1 - 0.0105 = 0.9895

Part c)

Mean = n * P = ( 10 * 0.7 ) = 7