Answer:
The teacher should set the score 7 as the lowest passing grade.
Step-by-step 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:
[tex]P(X=x)={10\chose x}0.50^{x}(1-0.50)^{10-x};\ x=0,1,2,3...[/tex]
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.
