Suppose that a random sample of 10,000 observations is taken from the normal distribution with unknown mean

Question:

Suppose that a random sample of 10,000 observations is taken from the normal with unknown mean μ and known variance is 1, and it is desired to test the following hypotheses at the level of significance 0.05:
H0: μ = 0,
H1: μ = 0.
Suppose also that the test procedure specifies rejecting H0 when |n| ≥ c, where the constant c is chosen so that Pr(|n| ≥ c|μ = 0) = 0.05. Find the probability that the test will reject H0 if
(a) The actual value of μ is 0.01.
(b) The actual value of μ is 0.02. Distribution
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