A study employs this distribution to model X-3-day flood volume (108 m3). Suppos

Question

A study employs this distribution to model X-3-day flood volume (108 m3). Suppose that values of the parameters are -11.: 8-Y-37 (very close to estimates in the cited article based on past data) What are the mean value and standard deviation of X? (Round your answers to four decimal places.) mean standard deviation 26.533 (a) 108m3 108m3 125 (b) What is the probability that flood volume is between 100 and 154? (Round your answer to three decimal places.) 6885 (c Round your answer to three decima what is the probability that flood volume exceeds its mean value by more than one standard de a o 156 places. (d) What is the 95th percentile of the flood volume distribution? (Round your answer to two decimal places.) 172.5x 10°m3 Need Help? Read It Talk to a Tutor

Explanation / Answer

From the standard table of z-score percentile for normal distribution, the z-score corresponding to 95 percentile is 1.645.

We know that z = (X-mean)/(standard deviation)

=> X = (z*standard deviation)+mean

In the given question, mean = 125 and standard deviation = 26.533

=> X = (1.645*26.533)+125 = 168.6468

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