On a homework question after i found the test value236 it th

On a homework question after i found the test value(2.36) it then asked for the p - value. On the answer it stated:

The area corresponding to 2.36 is .4909...from the table

Now, subtract .5 and get .0091

Thus, the p value = 2(.5 - .4909)

=2(.0091)

=.0182

I do not understand why they multiplied it by 2 as well as subtracted by .5?

Other info that might help answer this is as follows:

- sample of 50 players

- mean = 230

- standard deviation = 15

- alpha = .01

In hypothesis testing for two tailed test we have to double the p-value.

now the test value is 2.36.

here they used table for area between mean and z.

therefore they get 0.4909

but usually we used table for area beyond z.

As we know total area under the curve is equal to 1.00 or unity. Half of the area, or 0.50, is on either side of the mean.

therfore here they subtract 0.5 from 0.4909 to get area beyond z.

Or you can directly use table for area beyond z so that you will directly get 0.0091.

and since we have to find p value for two tailed test, its 2* 0.0091 = 0.182