Question

A literature professor decides to give a 10-questiontrue-false quiz to determine who has read an as-signed novel. She wants to choose the passing gradesuch that the probability of passing a student whoguesses on every question is less than .05. What score should she set as the lowest passing grade?

Answer 1

The teacher should set the score 7 as the lowest passing grade.

Explanation:

Let X = number of correct guesses.

All the questions are of true-false format.

The probability of getting a correct answer is, p = 0.50.

The total number of questions is, n = 10.

The random variable X follows a Binomial distribution with parameters n = 10 and p = 0.50.

The probability mass function of X is:

`P(X=x)={10\chose x}0.50^(x)(1-0.50)^(10-x);\ x=0,1,2,3...`

Now the teaches chose the grading scheme such that the probability of passing a student who guesses on every question is less than 0.05.

Then the probability of failing such a students is at least 1 - 0.05 = 0.95.

Compute the probability distribution of X.

Consider the probability distribution attached below.

The value of x for which P (X ≤ x) is at least 0.95 is, x = 7.

So the teacher should set the score 7 as the lowest passing grade.