Question

5.) Oh no! Jordan forgot to study for a multiple choice quiz. He has no idea what any of the correct answers are so he randomly guesses the answer for each question. There are 20 questions on the quiz, and each question has 4 possible choices, one of which is the correct answer.

(a) (8 pts) Find the exact probability that Jordan correctly guesses the answers to more than 7 questions. (b) (8 pts) Find the mean (expected) number of correct answers that Jordan gets on the quiz.

Answer 1

here this is binomial with parameter n=20 and p=P(getting correct answer =1/4 =0.25

a)

exact probability that Jordan correctly guesses the answers to more than 7 questions:

(Note:

if using ti-84 use command :1-binomcdf(20,0.25,7)

if using excel use command :1-binomdist(7,20,0.25,true)

b)

mean E(x)=μ=np=20*0.25 =5