Question

A true-false test has 40 questions. If a score of 36 (or more) correct is needed for an “A”, what is the probability of obtaining an “A” just by guessing? Hint – your outcome is not continuous. (10 points)

Answer 1

for abvoe probability of answering correct by guessing p=(1/2) (as there are two answer one of which is correct)

hence fron binomial distribution for which paramter n=40 and p=1/2

probability of obtaining an “A” just by guessing=P(X>=35)

=P(X=36)+P(X=37)+P(X=38)+P(X=39)+P(X=40)

=

=8.31*10^-8+8.99*10^-9+7.09*10^-10+3.64*10^-11+9.09*10^-13 =9.29*10^-08

( this can be solved by normal approximation too whcih will given probability ~0 ; please revert if you require this by normal distribution approximation)