Question

A quiz consists of 980 true or false questions. If the student guesses on each question, what is the mean number of correct answers? O 490 196 980 00 245 None of these

Answer 1

Given : n=980

Since , the questions are true or false type questions.

i.e. there are only two possibilities of correct answer.

Here , the answer is true or false is equally likely.

Now , The questions are independent.

Let , X be the number of correct answer.

Here , X has binomial distribution with parameter n=980 and p=0.5

Therefore , the mean of the binomial distribution is ,

Mean=np=980*0.5=490

Therefore , the mean number of correct answer is 490