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grin007 [14]
3 years ago
9

A literature professor decides to give a 10-questiontrue-false quiz to determine who has read an as-signed novel. She wants to c

hoose 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?

Mathematics
1 answer:
Darya [45]3 years ago
7 0

Answer:

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

Step-by-step explanation:

Let <em>X</em> = number of correct guesses.

All the questions are of true-false format.

The probability of getting a correct answer is, <em>p</em> = 0.50.

The total number of questions is, <em>n</em> = 10.

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

The probability mass function of <em>X</em> 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 <em>X</em>.

Consider the probability distribution attached below.

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

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

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