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 ì (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.