The marks in an examination for a physics paper have normal distribution with mean μ and variance σ2 . 10% of the students obtain more than 75 marks and 20% of them obtained less than 40 marks. find the value of μ and σ

Let be the random variable for the number of marks a given student receives on the exam.

10% of students obtain more than 75 marks, so

where follows a standard normal distribution. The critical value for an upper-tail probability of 10% is

where denotes the CDF of , and denotes the inverse CDF. We have

Similarly, because 20% of students obtain less than 40 marks, we have

so that

Then are such that

and we find

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

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1. perpendicular

2. parallel

3. perpendicular