A multiple choice test consists of 9 questions with 5 choices for each answer. A

Question

A multiple choice test consists of 9 questions with 5 choices for each answer. Assume that a student guesses all questions randomly. The random variable, X, is the number of correct guesses. The correct distribution for X is A. N(9, 5) B. N(9, 0.2) C. B(9, 0.2) D. t_g Find the probability that the student guesses no more than 3 questions correct? A. 0.0856 B. 0.3333 C. 0.9144 D. 0.1762 Over the long run of taking such an exam, on average how many questions would you expect a student to get correct by guessing randomly on each question of the test? A. 1 B. 2 C. 1.8 D. 2.2

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
Q36.
X ~ B(9,0.2)
Q37.
P( X < = 3) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 9 3 ) * 0.2^3 * ( 1- 0.2 ) ^6 + ( 9 2 ) * 0.2^2 * ( 1- 0.2 ) ^7 + ( 9 1 ) * 0.2^1 * ( 1- 0.2 ) ^8 + ( 9 0 ) * 0.2^0 * ( 1- 0.2 ) ^9
= 0.9144
Q38.
expected correct

Mean ( np ) =9 * 0.2 = 1.8

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