Suppose that, for a certain exam, a teacher grades on a curve. It is known that the mean is 50 and the standard deviation is 5.
There are 45 students in the class.
If an exam paper if selected at random, what is the probability that it will be a failing paper?
There are 45 students in the class.
If an exam paper if selected at random, what is the probability that it will be a failing paper?
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Assume that the test is out of 100 marks, and the passing grade is 50
Assume that the distribution of the exam marks is normal as well.
Let X = grade of a exam paper
X~normal(50 , 5^2)
P(paper is a failing paper)
= P(X < 50)
= P(Z < (50 - 50) / 5)
= P(Z < 0)
= 1 - P(Z >= 0)
= 1 - 0.5
= 0.5
Assume that the distribution of the exam marks is normal as well.
Let X = grade of a exam paper
X~normal(50 , 5^2)
P(paper is a failing paper)
= P(X < 50)
= P(Z < (50 - 50) / 5)
= P(Z < 0)
= 1 - P(Z >= 0)
= 1 - 0.5
= 0.5