Suppose that the amount of time CU Denver students spend engaged in their MATH 2830 coursework each week is normally distributed with a mean of 5.4 hours and standard deviation of 1.5 hours. 1. Draw a sketch of this population distribution with the values for , u o, u 1 20, and u + 30 clearly labeled. 2. If one of these students is selected at random, determine the probability that the student spends between 5 and 6 hours engaged in MATH 2830 coursework each week. In addition to the probability, your solution should contain a probability statement in terms of hours (X), a congruent probability statement in terms of standardized values (2), and support for the how you obtained those standardized values. Klie CU Denver Fall 2022 Math 2830 WA 6 Now suppose we take a random sample of 25 of these students and calculate the average time they spend engaged in MATH 2830 coursework each week. 3. Draw a sketch of the sampling distribution of these sample means with the values for u, u + u +2-, and u + 3- clearly labeled. 4. Determine the probability that the sample mean for these 25 students is between 5 and 6 hours. In addition to the probability, your solution should contain a probability statement in terms of the sample mean ( X ), a congruent probability statement in terms a standardized value (Z), and support for the how you obtained the standardized value