I am having trouble with a question that asks: What sample size is needed if the probability of not detecting a change of one standard deviation is to be no more than 1%.

So the hypotheses is two sides, i.e H_{0}:mu=mu_{0}and H_{1}: mu is not equal to mu_{0}. So H_{0 }is rejected if |Xbar-mu|>c

I started by setting the Pr(|Xbar-mu|=1 standard deviation) ≤0.01 =beta (type 2 error)

=>Pr(Z=sqrt(n))≤ 0.01

=> sqrt(n)

So I am stuck here i know n must be discrete. I am unsure how to proceed, or whether the previous steps I took were correct.

I would appreciate any help. Thanks in advance.