Why the critical probability p is calculated in this form?

I believe your confusion here stems from the difference in looking for a p value from 1 tail vs 2 tails. As you can see in the below illustration, we are only looking for the right side 30% that live longer than 30 days. Because we are only looking at one side, there is not a need to divide by two.

So we get a Z value for p= .7 of 0.524. From there we can use algebra in the Z= (x-Mu)/SD to get a standard deviation of 8.