Question

set of data is normally distributed with a mean of 200 and standard deviation of 50.
· What would be the standard score for a score of 300?
· What percentage of scores is between 200 and 300?
· What would be the percentile rank for a score of 300?
(Points : 6)

Answer 1

1) 300 is two deviations of 50 away from 200, so the standard score is 2.

2) You need to look at a normal distribution for this. A quick google search should help you just fine. Or, possibly, you were provided one in class.

From such a table, you can see that being two deviations away from the middle amounts to 34.13% + 13.59% = 47.72%

3) You just take 47.72% 9which is the distance from the middle to 300) and add 50% (which is everyone below the middle). You get 97.72%

Answer 2

1. Z (a standard score) = (score-mean/SD)

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.

Percentile rank is the proportion below or equal to a particular score.