hypothesis testing

In example 12.3 why have they added .5 as the continuity corrected....and not deducted .5 ?
Why p(z<-.712) has been taken and not p(z>-.712)?

 

The mean of our distribution under Ho will be: nq
i.e. 0.2*250= 50
Therefore mean is 50.
We always adjust d value of X towards the mean of the distribution under Ho and here our mean is greater than the observed value; 45 < 50....that is the reason why we add 0.5 to 45 rather than subtracting it.

 

Had the mean of the distribution be ,let say 40 we would have subtracted 0.5 from 45 as 40 < 45.

 

Thankyou
What Abt the poisson then given on the next page?