Find the cutoff score

Question

A reading program is targeting the lower 5% of students based on a reading test. If the average score for all students is 122.6 and the standard deviation is 18, find the cutoff score for those that will qualify. Assume the scores are normally distributed.

Answer 1

Hi Patricia! Thanks for the question.

The quickest way to do this is with a calculator such as the TI-84 Plus using the Inverse Normal (invNorm) function. On most versions of this calculator we would press 2ND, then VARS, then look for the invNorm function from the list shown and select it. It will then want us to enter 3 numbers: .05 (this is the 5% lower level from the problem), 122.6 (the average score), and 18 (standard deviation).

Depending on the calculator model it may ask us to enter these values into a list:

area: .05

µ: 122.6

o: 18

Or it will ask for a list separated by commas: invNorm(.05,122.6,18).

Either way the answer is 92.99, or rounded to 93, the cutoff score needed to qualify.

There is also a longer way to do it using a normal distribution table and calculating a “Z-score” which we can use if a calculator is not allowed. Since these tables vary by teacher, I would be happy to visit in a 1-on-1 appointment to walk us through.

Good luck!

Joe