Suppose that a single observation X is taken from the normal distribution with unknown mean and known variance is 1. Suppose that it is

Suppose that a single observation X is taken from the normal distribution with unknown mean μ and known variance is 1. Suppose that it is known that the value of μ must be −5, 0, or 5, and it is desired to test the following hypotheses at the level of significance 0.05:
H0: μ = 0,
H1: μ =−5 or μ = 5.
Suppose also that the test procedure to be used specifies rejecting H0 when |X| > c, where the constant c is chosen so that Pr(|X| > c|μ = 0) = 0.05.
a. Find the value of c, and show that if X = 2, then H0 will be rejected.
b. Show that if X = 2, then the value of the likelihood function at μ = 0 is 12.2 times as large as its value at μ = 5 and is 5.9 × 109 times as large as its value at μ=−5.