Question

5. A class of undergraduate criminal justice students took a test and the average score of the class was 280 with a standard deviation equal to 40.

1. What minimum score does a student need to obtain in order to pass the exam? (60^th percentile and above)
2. What is the minimum score a student need to receive in order to get at least a B (80^th percentile) at the exam?

Answer 1

The score of the class has mean = 280 and standard deviation = 40

a) Minimum score to pass the exam that is 60th percentile and above

60th percentile have 60% data below it. That is 0.60

So first find the z score using the standard normal table.

Search 0.60 or it's more closer value inside the body of that table and then take the corresponding row and column number.

the more closer value of 0.60 in the table is 0.5987, which occur at 0.2nd row and 0.05th column, so the z score is 0.2 + 0.05 = 0.25

That is z = 0.25

The formula of z score is,

Rearranging the formula in terms of x is,

Therefore, the minimum score does a student need to obtain in order to pass the exam is 290

b) At least B grade that is 80th percentile.

80th percentile means there is 80% data below that.

First find out the z score for 0.80, search 0.80 or it's closer value in the body of z table

0.7995 is more closer to 0.80, which occurs in 0.8th row and 0.04th column, so the z score is 0.8 + 0.04 = 0.84

z = 0.84

The formula to find the score x is,

The minimum score a student need to receive in order to get at least B grade at the exam is 313.6