Use this z-score formula for this problem:

z = (x - mean)/(sd/√n)

x = 1.25, 1.50
mean = 1.35
sd = 0.25
n = 40

Calculate two z-scores, then use a z-table to determine probability between the two scores.

I hope this will help get you started.

•stats. - Christina, Monday, March 18, 2013 at 9:57pm
z=(1.25-1.35)/(0.25sqrt40)= -0.0791
z=(1.50-1.35)/(0325sqrt40)= 0.0791

but not sure how to read the z scores I don't know if it would be.5000-.5000 or what can someone please help me on the z scores for -0.0791 and 0.0791

Thank you

I have never seen your formula for z-scores

Every place you look, in every textbook, you will find
z = (x - mean)/sd

anyway, I noticed that your formula has a denominator of (sd/√n) but in your calculations you did (sd√n)

looking at your calculations , where did the 0325 come from in your second z score calculation?

taking your formula at face value:
z1 = (1.25 - 1.35)/(.25/√40) = -2.05298
z2 = (1.5 - 1.35)/(.25/√40) = 3.7947

suppose these are "correct" you will now go to your tables or chart. (I don't have any in front of me)
using the 3 signifiant digits, go down the column to -2.0, then across that row to (.-5)
You should have an entry of appr .0202
now find 3.7 in the column and go across to .09 to fins
an entry of appr .9999

so the prob between the two z-scores
= .9999 - .0202
= .9797

In any case, I don't think that answer is even close.
Your formula must be wrong.

Your formula with SD/√n is for a distribution of means. Dividing solely by SD is for a distribution of raw scores.

Which divisor you use depends on how the problem is phrased.

To find the probability between the two z-scores (-0.0791 and 0.0791), you need to use a z-table. A z-table provides the cumulative probability up to a certain z-score.

First, let's determine the area to the left of each z-score:
For z = -0.0791:
- Look for the absolute value of the z-score in the z-table. In this case, look for 0.0791.
- The z-table will give you the cumulative probability from the left. In this case, the z-table should give you approximately 0.4681.

For z = 0.0791:
- Again, look for the absolute value of the z-score in the z-table. In this case, also look for 0.0791.
- The z-table will provide the cumulative probability. In this case, the z-table should give you approximately 0.5319.

Now, to find the probability between these two z-scores, subtract the first probability from the second probability:
0.5319 - 0.4681 = 0.0638

Therefore, the probability between the two z-scores (-0.0791 and 0.0791) is approximately 0.0638, or 6.38%.

Remember, z-tables may differ slightly for specific decimal places, so it's always best to use a reliable and accurate z-table for precise calculations.