5. [2.1/5 Points] DETAILS PREVIOUS ANSWERS DEVORESTAT9 4.4.066. MY NO The two-parameter gamma distribution can be generalized by introducing a third parameterly, called a threshold or location parameter: replace x in (4.8), ((x; a) - [(a) X 2 0 (4.7) otherwise by x - y and x 2 0 by x _ y. This amounts to shifting the density curves in the figure below so that they begin their ascent or descent at y rather than 0. 1.0 a = 2, B-! 0.5 1.6 a-2, B-1 (a) gamma density curves standard gamma density curves A study employs this distribution to model X - 3-day flood volume (10 m ). Suppose that values of the parameters are a - 11, | 8, y- 38 (very close to estimates in the cited article based on past data). (a) What are the mean value and standard deviation of X? (Round your answers to four decimal places.) mean standard deviation 26.5330 (b) What is the probability that flood volume is between 100 and 153? ( Round your answer to three decimal places.) 0.709 X What is the probability that flood volume exceeds its mean value by more than one standard deviation? ( Round your answer to three decimal places.) 0.156 (d) What is the 95th percentile of the flood volume distribution? (Round your answer to two decimal places.) 141.5876 X 108m 3