Question 1073285
alpha on the left is .0015
alpha on the right is .025


z-score on the left is -2.968
z-score on the right is 1.96


z-score for the mean is 0.


the difference between the high z-score and the low z-score is equal to 2.968 + 1.96 = 4.928


the difference between the high raw score and the low raw score is equal to 377 - 347 = 30.


the standard deviation of the raw score should be 30 / 3.928 = 6.087662338


if that's true, than you can solve for the mean as follows:


z = (x-m)/sd


solve for m in this formula as follows:


start with z = (x-m)/sd


multiply both sides by sd to get z * sd = x - m


subtract x from both sides to get z * sd - x = -m


multiply both sides by -1 to get -z * sd + x = m


rearrange the terms to get x - z * sd = m


commute the equation to get m = x - z * sd


with the low raw score and the low z-score and the calculated sd, this formula becomes:


m = 347 - (-2.968 * 6.087662338 = 365.0681818


with the high raw score and the high z-score and the calculated sd, this formulabecomes:


m = 377 - 1.968 * 6.087662338 = 365.0681818.


that's your answer.


the mean is 365.0681818


the standard deviation is 6.087662338


the z-score calculator i used can be found at this link:


<a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


the following pictures show the calculations.


the first 2 pictures calculate the z-score from the percentages.


the second 2 pictures calculate the percentages from the z-score.


the third 2 pictures calculate the percentages from the raw score.


the percentages used and shown are the decimal equivalent of the percentages.


.15% = .0015
2.5% = .025


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