The scores on a test are normally distributed with a mean of 80 and a standard deviation of 5. Twelve students had test scores between 80 and 90. Estimate the number of students who took the test.

Question

The score range is between 0 to 100.

Answer 1

Aidan:

Find the z-score of 90. We know the mean is 80 and the standard deviation is 5.

z score of 90 = (90-80)/5 = 2

z-score of 2 represents 97.725 percentile (0.97725)

We know that 80 is the mean and so 50 percentile (0.5)

Then (0.97725-.5) = 0.47725 is the percentage of the total number of students that score between 80 and 90.

To find out the total number of students that took the test, solve 0.47725*x = 12 for x.