SOLUTION: A normal distribution has a mean of 85.8 and a standard deviation of 4.88. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.)
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-> SOLUTION: A normal distribution has a mean of 85.8 and a standard deviation of 4.88. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.)
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Question 1169227: A normal distribution has a mean of 85.8 and a standard deviation of 4.88. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.)
z = 0.65 Answer by Theo(13342) (Show Source):
z = (x - m)/sd
z = z-score
x = raw score
m = mean
sd = standard deviation.
when m = 85.8 and sd = 4.88 and z = .65, you get:
.65 = (x - 85.8) / 4.88
solve for x to get:
x = .65 * 4.88 + 85.8 = 88.972
if they're equivalent, they should have the same area under the normal distribution curve to the left of them.
confirm using a normal distribution calculator.
the one i used is the ti-84 plus.
z-score of .65 has an area of .7421539567 to the left of it.
raw score of 88.972 has an area of .7421539567 to the left of it.
you get the same area to the left of the z-score as the raw score, so the z-score and the raw score are comparable in their relationship to their position under the normal distribution curve.
here's a display of the z-score result and the raw score result.
the area to the left of each is the same.
to get the z-score result, make the mean = 0 and the standard deviation = 1.
to get the raw score result, make the mean = 85.8 and the standard deviation = 4.88.
the online calculator rounds the result to 3 decimal places.
this is usually sufficient.
