Question: The time it takes a student to complete a statistics homework assignment is continuous and uniformly distributed between the values of 40 minutes and 50 minutes. Determine the following:

a. (4) Give the equation of the density function and draw the graph of this continuous uniform distribution function. (You are required to label both axes of the graph.)

b. (2) What is the probability that it takes between 42 to 48 minutes for a student to complete the assignment?

c. (2) What is the probability that it takes more than 47 minutes for a student to complete the assignment?

d. (2)What is the probability that it takes 44 minutes exactly for a student to complete the assignment?

e. (2) What is the mean time for a student to complete the assignment?

f. (3) Use mathematical integration to show that the variance of the time for a student to complete the assignment is 3 minutes. (Calculator is OK but must show calculator commands and proper entries)