Question 1119446
population mean is 225.8
population standard deviation is 87.4
sample size is 215.


standard error = standard deviation divided by square root of sample size.


standard error = 87.4 / sqrt(215) = 5.960630527.


you look up in the normal distribution table, or use a normal distribution calculator, to find the z-score that is associated with 829% of the area under the normal distribution curve that is to the left of it.


i used the normal distribution calculator that is in the TI-84 Plus and came up with a z-score of .915365082.


to find the raw score associated with that, use 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 error.


that formula becomes:


.915365082 = (x-225.8) / 5.960630527.


solve for x to get:


x = .915365082 * 5.960630527 + 225.8.


that results in x = 231.2561531.


that score will have 82% of the normal distribution curve to the left of it and 18% of the normal distribution curve to the right of it.


that means the probability of getting a raw score less than 231.2561531 is 82% and the probability of getting a raw score greater than 231.2561531 is 18%.


visually, this looks like this:


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<img src = "http://theo.x10hosting.com/2018/070602.jpg" alt="$$$" >


the first display shows you the proability of getting a raw score less than 231.2561.


the second display shows you the probability of getting a raw score greater than 231.2561.


round your answer as required.


any difference between what this online calculator shows you and the calculator i used has to do how many decimal places rounding has occurred.