A toy maker company are making a new toy and is interested in toy height (in millimeters). The new toy height is approximately normally distributed, with standard deviation 30 millimeters. The company wishes to test whether the population mean is not equal to 179.0, using the results of 12 samples.

1.Find the type I error probability if the critical region lower and upper bounds are, respectively, 174 and 184.

2.Given the critical region in part 1, what is the probability of a type II error if the true mean toy height is 174.0?

3.Find when the true mean is 187.0.