Homework Soursea multiple choice quiz had 10 questions each with 4 alternat
a multiple choice quiz had 10 questions each with 4 alternatives. a passing score is 6 or more correct if a student attempts to guess the answer to each question. what is the probability she passes.
a multiple choice quiz had 10 questions each with 4 alternatives. a passing score is 6 or more correct if a student attempts to guess the answer to each question. what is the probability she passes.
a multiple choice quiz had 10 questions each with 4 alternatives. a passing score is 6 or more correct if a student attempts to guess the answer to each question. what is the probability she passes.
Solution
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
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 10 5 ) * 0.25^5 * ( 1- 0.25 ) ^5 + ( 10 4 ) * 0.25^4 * ( 1- 0.25 ) ^6 + ( 10 3 ) * 0.25^3 * ( 1- 0.25 ) ^7 + ( 10 2 ) * 0.25^2 * ( 1- 0.25 ) ^8 + ( 10 1 ) * 0.25^1 * ( 1- 0.25 ) ^9 + ( 10 0 ) * 0.25^0 * ( 1- 0.25 ) ^10
= 0.9803
P(probability she passes ) = P( X > = 6 ) = 1 - P( X < 6) = 0.0197
