PLEASE HELP!!
A set of test scores are normally distributed. Their mean is 100 and standard deviation is 20. These scores are converted to standard normal z scores. What would be the mean and median of this distribution?
a. 0
b. 1
c. 50
d. 100

Question

PLEASE HELP!!
A set of test scores are normally distributed. Their mean is 100 and standard deviation is 20. These scores are converted to standard normal z scores. What would be the mean and median of this distribution?
a. 0
b. 1
c. 50
d. 100

kropot72 · Answer

In a normal distribution, the mean and the median have the same value. The z-score of the mean is always zero.

ttop0816 · Answer

@kropot72  so would the median be also zero?

bunny12 · Answer

Doesn't it say their mean is 100?

ttop0816 · Answer

nono

mathmale · Answer

ttop0816:  I agree with you.  The 100 z-scores you obtain will be both positive and negative in sign, and will have a mean of zero.

Think about what "median" means in this context.  What do you suppose would be the median of your 100 z-scores?

mathmale · Answer

The mean of the original scores is 100, yes.  But the question goes on to ask what the mean of the z-scores is.

ttop0816 · Answer

Then to find the z-score, would I use this function to get it? 
z= (x-mean)/standard deviation

ttop0816 · Answer

@mathmale

jclark · Answer

Trick question almost. Z score = value minus mean all divided by standard deviation. Since the "value" is the mean, the z score is (100-100)÷20=0. And in order for a distribution to be normal, mean=median=mode. This question is testing whether or not you know these facts.

ttop0816 · Answer

@jclark thank you!