questions reads as follows:

sat scores around the nation tends to have a mean score around 500, a standard deviation of 100 points and are approximately normal distribution. a person who scores 600 on the sat has approximately what percentile rank within the population? please show all calculatons.

600-500=-100/100= 0.999999 would that be correct? if not how would you show the calculations?

*thank you very much.
mary hornbeck

Follow TutorCat's site to find

z=(x-xmean)/standard deviation
to get
z=(600-500)/100=1

http://mathworld.wolfram.com/z-Score.html

The next step is to look up a probability table, or use your calculator to find out the one-tail probability (i.e. every score lower than 600). For a probability table, try:

http://www.math.unb.ca/~knight/utility/NormTble.htm

to find that for z=1.0, the probability is 84.13%.

Notice that for z=0 (exactly in the middle of the normal curve, or the mean =500, the probability is 0.5.

To find the percentile rank of a score in a normal distribution, you need to calculate the z-score first. The z-score tells you how many standard deviations away from the mean a particular score is.

In this case, the mean score is 500 and the standard deviation is 100. To find the z-score for a score of 600:

Z = (X - mean) / standard deviation
Z = (600 - 500) / 100
Z = 1

Once you have the z-score, you can find the percentile rank using a z-table or a statistical calculator. The percentile rank represents the percentage of scores that fall below a particular score in a normal distribution.

Using a z-table, you can find that a z-score of 1 corresponds to approximately 84th percentile. This means that approximately 84% of the scores fall below a score of 600.

Therefore, a person who scores 600 on the SAT would have an approximate percentile rank of 84 within the population.