Amazon claims it delivers all prime shipments in an average of 2 days

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Amazon claims it delivers all prime shipments in an average of 2 days. You want to test whether this claim is true, or whether the true mean delivery time is actually longer than what they claim. You are planning on taking a sample of 100 deliveries, calculating a sample mean and running a hypothesis test to determine if their claim is false. The standard deviation of all delivery times is known to be .5 days from a previous study.

1)Design an appropriate hypothesis test, using alpha = .08 (don't run the test, just set up the null and alternative hypothesis and the appropriate rejection region)

2)What is the probability of a type one error for the test?

3)What is the probability that your test will commit a type two error, if the true mean

4)delivery time is 2.25 days