Question

Find the probability using the normal distribution:P(0<z<2.56). use the cumulative normal distribution table and enter the answer to 4 decimal places.

Answer 1

Generally in a normal distribution table the values in the table are to left of the Z-score

Here the Z-score is 2.56

I have attached the normal distribution tabe below

We need to look for 2,5 on the rows and 0.06 on the columns and look at where they are meeting to get the value from the table

The value for z-score 2.56 is 0.99477

But this area is from ( - infinity to 2.56)

But we want the probability for only 0 to 2.56

In a normal distribution half of the area is to the left of 0 and half of the area is to right of 0

So To get the probability for 0 to 0.26 we should subtract whole left side (let to 0) area of 0.5 from 0.99477

So P(0 < Z < 2.56) = 0.99477 - 0.5 = 0.49477

So the answer is 0.4948