Question

Assume that the number of multiple-choice questions I get correct out of 100 follows a binomial distribution with me just guessing with an equal probability for each answer (A-D). Find the exact probability of me getting 25 or less correct under these assumptions.

check if the CLT conditions are satisfied first, then find an approximate probability, assuming that the number of correct answers out of 100 follows a normal distribution.

Answer 1

Let , the total number of questions=n=100

Since , each question have a 4 multiple choices.

Out of 4 , one choice is correct.

Now , p be the probability that the correct choice

Therefore , p=1/4=0.25

Here , np=100*0.25=25>5 and nq=n(1-p)=100*(1-0.25)=75>5

Therefore , the condition of CLT are satisfied.

Now , we want to find the

Where , and

; From the standard normal probability table

Therefore , the probability of getting 25 or less correct 0.5