The mature height of blue aster plants treated with Sun’s Natural Energy plant food can vary between 10 and 18 inches, and has a uniform probability distribution over this range of values. Define the probability density function here and use it to do what’s required below: 

a. Determine the probability that the mature height of a treated plant will be between 16 and 17 inches. 

b. Determine the probability that mature height of a treated plant will be more than 17.8 inches. 

c. Determine the mean (expected value) and the standard deviation of the “mature plant height” random variable. 

d. Show that the total area associated with the probability density function here is 1.0. That is, demonstrate that P(10 ≤ x ≤ 18) = 1.0.