The producer of an electric machine wants to make a test to see how many of their machines that are working correct. The hypothesis are the following:

: the proportion of defect machines is at most 8%

: the true proportion of defect machines is more than 8%

The producer decides to reject

if the sample proportion of defect machines are more than 12%.

i) If we draw a sample of 100 machines, then what is the probability of making a type I error?

I'm thinking of a Z-transformation.

And then I look up P(Z>z) in a table. Is that correct?

ii) If we know that the true proportion of defective machines is 15%. Then what is the probability of a type II error with a random sample of 100?

Since this will be negative, I look up the probability that Z(<-z) in a table. Do I think in the right way?

Thanks a lot for your help.