SOLUTION: a set of data is normally distributed with a mean of 1000 and a standard deviation of 100 what would be standard score for a score of 900 what percent of scores is between 1000 and

Question 617669: a set of data is normally distributed with a mean of 1000 and a standard deviation of 100 what would be standard score for a score of 900 what percent of scores is between 1000 and 900 what would be percentile rank for a score of 900
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean = 1000
standard deviation = 100
standard score = z-score
standard score for 900 would be equal to:
(900 - 1000) / 100 = -1.0
A score of 900 is 1 standard deviation below the mean which would have a standard score of 0.
the area to the left of a z-score of -1 is equal to .1587
the area to the left of a z-score of -0 is equal to .5
the area between a z-score of 0 and a z-score of -1 is therefore equal to .5 - .1587 which is equal to .3413.
since a z-score of -1 is equivalent to a score of 900 and a z-score of 0 is equivalent to a score of 1000 for this problem, this means that 34.13% of the area under the normal distribution curve is between 900 and 1000.
The percentile rank of a score of 900 would be equal to 15.87% because a score of 900 is better than 15.87% of all the scores.
here's a reference on percentile rank.
http://davidmlane.com/hyperstat/A79567.html
here's a reference on z-scores.
http://www.measuringusability.com/zcalc.htm
here's a reference on normal distribution curves
http://www.regentsprep.org/Regents/math/algtrig/ATS2/NormalLesson.htm

RELATED QUESTIONS
a set of data is normally distributed with a mean of 200 and standard deviation of 50.... (answered by richard1234)

a set of data is normally distributed with a mean of 1000 and standard deviation of 100. (answered by stanbon)

A set of data is normally distributed with a mean of 1000 and standard deviation of 100. (answered by stanbon)

A set of data is normally distributed with a mean of 200 and standard deviation of 50.... (answered by robertb)

A set of data is normally distributed with a mean of 100 and standard deviation of 15. (answered by solver91311)

I am not understanding... A set of data is normally distributed with a mean of 100... (answered by ewatrrr)

A set of data is normally distributed with a mean of 1,000 and standard deviation of... (answered by stanbon)

A set of data is normally distributed with a mean of 500 and standard deviation of 100. (answered by edjones)

A set of data is normally distributed with a mean of 500 and standard deviation of 100. (answered by stanbon)