# I need help with this problem

#### maravillas33

##### New Member
if I have the mean of a test score 68 and sd 28, and they are asking me to find the proportion of student thar got less than 48. It is that 48-68/28 ??? How do I do this.

#### superdix

##### New Member
Maravillas,

This gives you a Z value of (68-48)/28, which is 0.714. The Z value basically tells you how many standard deviations from the mean your wanted number is -- in your case, 48 is 0.714 standard deviations below the mean. The next thing to do is either look up this value in a table of Z values, or use a calculator.

Now, because 48 is below the mean, you need to use a negative Z value (-0.714).

In case you use the same calculator as me, the Casio FX-series, here's how:
1. Find the P( function by pressing OPTN - > - PROB - > P(
2. Type in -(68-48)/28)
3. Press EXE. Result will be 0.238 or 23,8%.

If you want to use a table, try to find one that has both positive and negative Z values. If it has only positives, 0.714 will yield 0.762 or 76,2%. This doesn't make much sense, of course, seeing as 48 lies below the mean. To get the correct answer using a table, you need to subtract 0.762 from 1, which equals 23,8%.

Hope that helps.
Richard

Last edited: