Question: Example concerned selecting random samples of n 5 190 from a population of student responses to the question "How many hours of sleep did you get last night?" Suppose that in a large population of students, the mean amount of sleep the previous night was μ = 7.05 hours and the standard deviation was σ = 1.75 hours. Consider randomly selected samples of n = 190 students.

a. What is the value of the mean of the sampling distribution of possible sample means?

b. Calculate the standard deviation of the sampling distribution of possible sample means.

c. Use the Empirical Rule to find values that fill in the blanks at the end of the following sentence: For 68% of all randomly selected samples of n = 190 students, the mean amount of sleep the previous night will be between _ _ _ _ _ _ _ and _ _ _ _ _ _ _ hours.

d. Use the Empirical Rule to fill in the blanks at the end of the following sentence. For 95% of all randomly selected samples of n = 190 students, the mean amount of sleep will be between _ _ _ _ _ _ _  and _ _ _ _ _ _ _ hours.

Example: Mean Hours of Sleep for College Students The sample of Penn State students first included the question "How many hours of sleep did you get last night?" The mean of the 190 responses was 7.1 hours. Suppose that we were to ask another 190 students that same question. It is unlikely that the mean response would be exactly 7.1 hours again.