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...](https://tex.z-dn.net/?f=P%28X%3Dx%29%3D%7B10%5Cchose%20x%7D0.50%5E%7Bx%7D%281-0.50%29%5E%7B10-x%7D%3B%5C%20x%3D0%2C1%2C2%2C3...)
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.