According to the Bureau of Labor, the average American aged 15 years or older gets 8 hours and 23 minutes (503 minutes) of sleep per night. To test if this average has changed recently, a random sample of 55 Americans aged 15 years and older was selected, and the number of minutes they slept recorded. Assume the standard deviation of hours of sleep is 60 minutes. Using σ = 0.02, answer the following questions:

a. Explain in your own words how Type I and Type II errors can occur in this hypothesis test.

b. Calculate the probability of a Type II error given the actual average hours of sleep is 524 minutes.

c. Calculate the probability of a Type II error given the actual average hours of sleep is 500 minutes.