Calculating the Probability of Type II Error

A sample of 200 items will be taken and the population standard deviation is σ; = 10. Use α = .05. Compute the probability of making a Type II error, if, unbeknownst to the tester, the real mean is 18.
Show all work and include a sketch that represents β.

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... the tester, the real mean is 18.
Show all work -- include a sketch that represents β as an area under the PDF.
Solution:
Our task is to calculate  when  = 18 and  = 10

Our first task is to set up the rejection region in terms of xbar. ...