Question 1137009
the mean is 148.3 and the standard deviation is 92.3.


128.6 is equal to (148.3 - 128.6) / 92.3 = .2134344529 standard deviations below the mean.


since the mean in a z-score is 0 and the standard deviation in a z-score is equal to 1, then the z-score for 128.6 with a mean of 148.3 is equal to 0 - .2134344529 = -.2134344529.


you can confirm this using the z-score formula of z = (x - m) / s.


z is the z-score
x is the raw score
m is the mean
s is the standard deviation in this case.


you get z = (128.6 - 148.3) / 92.3 = -.2134344529.


if you use a z-score calculator to get the probability of getting a z-score less than -.2134344529, the calculator will tell you that the probability is equal to .4154940862.


that would be your solution if you were talking about a raw score of 128.6.


if you are talking about a raw score of minus 128.6, you would get a totally different answer.


in that case, z = (-128.6 - 148.3) / 92.3 gets you z = -3.


if you use a z-score calculator to get the probability of getting a z-score less than -3, the calculator will tell you that the probability is equal to 
.0013499672.


i used the normal distribution calculator in the TI-84 Plus to get these numbers.


there is an online calculator that will do the calculations for you and give you a visual display of the results.


it does round a bit more than the TI-84 Plus, but the answer will be reasonably close if you take the rounding into consideration.


that calculator can be found at <a href = "" target = "_blank"></a> and the results of the analysis are shown below.


the calculator can be used with z-score or it can be used with raw scores.


if used with z-scores, the mean is 0 and the standard deviation is 1.


if used with raw scores, the mean is the actual mean and the standard deviation is the actual standard deviation.


i used the area from a value part of the calculator and i did z-scores first and then raw scores to show you the difference and the fact that you get the same answer give or take a few due to possible rounding differences.


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