Question

A quiz for a Psychology class consists of 5 questions. The questions are multiple-choice with 4 possible answers each, with only one correct answer. A student randomly guesses on all 5 questions.

1. create a probability distribution for the number of correct answers
2. what is the probability that the student will pass with a 60% or better
3. what is the probability that the student will answer less than 4 correct

Answer 1

Sample size , n =    5
Probability of an event of interest, p =   0.25

Binomial Probability Distribution4

what is the probability that the student will pass with a 60% or better

= P(X>=3)

	X	P(X)
P ( X = 3) = C (5,3) * 0.25^3 * ( 1 - 0.25)^2=	3	0.0879
P ( X = 4) = C (5,4) * 0.25^4 * ( 1 - 0.25)^1=	4	0.0146
P ( X = 5) = C (5,5) * 0.25^5 * ( 1 - 0.25)^0=	5	0.0010

= 0.1035

what is the probability that the student will answer less than 4 correct

= P(X<4)

	X	P(X)
P ( X = 0) = C (5,0) * 0.25^0 * ( 1 - 0.25)^5=	0	0.2373
P ( X = 1) = C (5,1) * 0.25^1 * ( 1 - 0.25)^4=	1	0.3955
P ( X = 2) = C (5,2) * 0.25^2 * ( 1 - 0.25)^3=	2	0.2637
P ( X = 3) = C (5,3) * 0.25^3 * ( 1 - 0.25)^2=	3	0.0879

=0.9844

THANKS

revert back for doubt

please upvote