5. [2.1/5 Points] DETAILS PREVIOUS ANSWERS DEVORESTAT9 4.4.066. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The two-parameter gamma distribution can be generalized by introducing a third parameter 3/, called a threshold or location parameter: replace X in (4.8), Xalex 7 2 O fiX: a) = m) X (4.7) 0 otherwise by x y and x 2 0 by x 2 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. fix: a. {:5} fit: u i ' 1.0 I.O /L. = 1 g u = .6 O" 0.5 3 / a = " /u = S 0 ' 0 I I l 'l_ | ' ' i 2 1 4 5 (a) gamma density curves (b) standard gamma density curves A study employs this distribution to model X = 3-day ood volume (108 m3). Suppose that values of the parameters are a = 12, ' = 6, y = 37 (very close to estimates in the cited article based on past data). A study employs this distribution to model X = 3-day ood volume (108 m3). Suppose that values of the parameters are a = 12, {3 = 6, y = 37 (very close to estimates in the cited article based on past data). (a) What are the mean va ue and standard deviation of X? (Round your answers to four decimal places.) mean 109 / 108m3 standard deviation 20.7846 / 108m3 (b) What is the probability that flood volume is between 100 and 1527 (Round your answer to three decimal places.) 0.658 x (c) What is the probability that flood volume exceeds its mean value by more than one standard deviation? (Round your answer to three decimal places.) 0.028 x (d) What is the 95th percentile of the flood volume distribution? (Round your answer to two decimal places.) 1.152 x 10%3 weed Hem/2 @ m Submit