Statistics Question

Question

At Saint Algebra College, the 200 freshmen enrolled in introductory biology took a final exam on which their mean score was 72 and their standard deviation was 6. Below are the grades of 10 students. Convert each into Z scores and determine the number of people who scored higher or lower than each other 10 students.

	Z score	Number of student above	Number of student below
60	-2
57
55
67
70
72
78
82
90
95

Answer 1

In order to compute the Z score on these you want to use the equation

Z = (x – mean) / (standard deviation)

So for each of the test scores in this set of information that means taking

Z = (x – 72) / 6 in order to compute what the value would be.

So like for 57 for example, that calculation is

Z = (57 – 72) / 6 = -2.50

For the placement out of the 200 then you can convert the Z score into a p-value using either a normal distribution table or software like Excel, then multiply by 200.

So like for the example row of the score of 57, if you check on a Z table the p-value for the score of -2.5 is 0.0228. That means that 0.0228 * 200 = 5 students scored below that percentage.

And then 200 – 5 = 195 scored above.

You can apply that same logic to the remaining rows! :)