The scores of students on a standardized test form a normal distribution with a mean of 140 and a standard deviaition of 12. If 36000 students took the test, how many scored above 149?

Answer 1

You need to first find the probability that a single student scores above 149.

To do this we first need to find the z-score associate with 149.

z = x-µ . where µ is the mean and σ is the standard deviation

σ

z = (149-140)/12 = 9/12 or .75

Once you have the z-score you need to determine the probability associated with that z-score is .7734

But this is the probability of being less than a z of .75 or being less than 149.

Since this question is the probability of being greater than 149, we need to subtract that probability from 1.000

1.0000 - 0.7734 = 0.2266

Now we have 36,000 students and 22.66% area expected to score above 149

36000 x .2266 = 8157.6 or 8,158 students.