My attempt:

a) Test statistic: Z = (X bar - 13) / (4/sqrt n)

Let μ = μ_a > 13 be a particular value in H_a

Power(μ_a)

= 1- beta(μ_a)

= P(reject Ho | H_a is true)

= P(reject Ho | μ = μ_a)

= P(Z>1.645 | μ = μ_a)

= P(X bar > 13 + [(1.645 x 4)/(sqrt n)] | μ = μ_a)

I also know that X bar ~ N(μ, 16/n)

I am stuck here...How can I proceed from here and express the power in terms of μ and n?

Thank you very much!

Note: this topic is also under discussion in SOS mathematics cyberboard