Can someone help me figure out this normal z-score? (statistics)?

Question

Scores on a math achivement test are normally distributed with a mean of 150 and standard deviation of 30.

Whatis the score of a peron who scored lower than 97.5% of all scores?

( I think this is a reverse z-score, and if it is, I think i missed the class we learned that).

To the first two posters, thank you! Although your post was pretty starightforward poster #1 and am thankful for it, I found poster #2's post to be more thorough. THANK YOU!!!!!!! You both are life savers!!!!

Answer 1

Look in your normal table and get the Z for 0.975 (it's 1.960)

Then convert that to a score for you population:

Z = (s-mean)/sd

s = Z*sd+mean

This means that 97.5% of the population scored less than this s.

Answer 2

First of all, how you find the answer depends on the type of z-table that you are using. Try looking up 1- 0.975 inside the table. The z-value corresponding to 0.025 is 1.96.

z = (value - mean) / stand dev

Plug everything in and solve for the value:

1.96 = ( value - 150) / 30

multiply both sides by 30

58.8 = value - 150

add 150 to both sides

value = 208.8