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Question 613:

I am confused on how to calculate a z-score. I am doing a six sigma project right now and am lost on doing the z-score. Here is the information I am provided:

Calculate the average student score necessary for the district to retain its federal funding.
(You may assume the standard deviation will not change). This will require some
thought. Think of the z formula. You will be solving for (average test score in the next
school year.)
Think about what you already know. You know the standard deviation (because we assume
that the variation in test scores stays approximately the same across years.)
You also know that 70% of students must meet the cut off score.

Data:
The following are the results from last years MEAP scores for EHS
N = 1000
x = 69.7
sd = 11.55

A student must score at or above 70% on the MEAP to meet the president's cut off score

Project Information:

The improvement program No Child Left Behind legislation has placed emphasis
on testing students, and has tied federal funding (and thus some matching state funds) to a certain
percentage of students meeting or exceeding cut off scores on state level achievement tests.
The challenges that face education are very interesting indeed: unlike in manufacturing
(where Six Sigma methodology was originally developed) the outcome is not a product that
meets stated specifications, rather it is a student who is prepared to take his/her place in society.
Unfortunately, the definition of prepared is elusive. Also unlike in manufacturing, public
educational institutions cannot reject the materials they receive (students) as being defective
and send them back they must take students at whatever point they received them, and advance
their state of preparedness.
The challenge for this project revolves around Everyday High School in Normal, Michigan.
Last year only 49% of the students at the high school met the cutoff score of 70%
of questions answered correctly on the Michigan Educational Assessment Program (MEAP)
Michigans state level test. This percentage of students meeting the cutoff score is well
below the 70% of students who must meet the cutoff score for the district to continue to receive
federal funding. Because losing the federal funding (approximately $2,000,000 per year)
would mean cuts in programs and maybe even staff that the board of education (BOE), parents,
community, students, and staff would find unacceptable, the board of education has directed
you (the Six Sigma Black Belt) to conduct a project to improve the scores on next years
MEAP tests.

If you need help with the concepts covered in this question (like z-scores and the normal-curve) you can download a visual and easy to understand Crash Course in Z-scores and an Excel Calculator which will do everything you need to do with z-scores.

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