A sample of 150 statistics students reported the typical number of hours that they sleep on a weeknight. The mean number of hours was 6.65, and the standard deviation was 1.24. (For this exercise, treat this sample as the entire population of interest.) 

a. What is always the mean of the z distribution? 

b. Using the sleep data, demonstrate that your answer to part (a) is the mean of the z distribution. 

c. What is always the standard deviation of the z distribution? 

d. Using the sleep data, demonstrate that your answer to part (c) is the standard deviation of the z distribution. 

e. How many hours of sleep do you typically get on a weeknight? What would your z score be, based on this population?