Question

The marks of students taking a statistics examination is normally distributed with a standard deviation of 10 marks. 10% of students scored above 85 marks for the examination. Determine the percentage of students who scored above 65 marks for the examination.

Answer 1

Let X be the random variable indicating the score of the student in the exam.

The standard deviation = 10.

We know that

P(X > 85 ) = 0.1

This implies

P(X <= 85) = 1 - 0.1 = 0.9

Now, consider the standard normal variable z which is

Using this, we get

From the table for the standard normal variable, we get

z1 = 1.28

Comparing this value with the previous equation, we know that

We need to calculate

P(X > 65) = 0.76424