Question

# A quiz for a Psychology class consists of 5 questions. The questions are multiple-choice with 4...

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

#### Homework Answers

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

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