stats test question?

Question

this was a question on my test today, and i just wanna compare my answer to everyone elses:

mean of 100 Standard deviation of 15 "i" scored in the 70th percentile, what is my raw score?

please answer only if you know what you are talking about, and if you could explain how you got to that answer it would be even more helpful
thanks all!

Answer 1

Is this an IQ question? Sounds like it.

70th percentile refers to a z-score of .5244. What's a z-score? It's a standardized statistic calculated using a raw score, the population mean, and the population standard deviation. To skip the mumbo-jumbo, the z-score is another way of helping you compare how you did against everybody else.

To convert from z-score to raw score, you have to know the mean and sd. Fortunately, you have these. Here's what you do:

let x = raw score

z = (x - mean) / sd; solving for x, we get

(z * sd) + mean = x

In your example, x = (.5244*15) + 100 = 7.866 + 100 = 107.866

You scored about a 108.

Answer 2

First convert the 70% [0.70] to a "Z-score", using the inverse standard normal distribution. Use calculator or table to find that

0.70 = Ph(0.525)

In other words, your score lies 0.525 times the standard deviation above the mean:

score = 0.525 x 15 + 100 = 7.875 + 100
= approx. 108

Answer 3

Would it be 70% of 85?