Question

1. The annual precipitation measurements (Pi in cm) for M city, over a 20year period are shown in the following table. Determine the mean, standard deviation, and skew coefficient for this series.

Year	Pi(cm)	Year	Pi(cm)
1999	44.2	2010	39.2
2000	47.6	2011	38.3
2001	38.5	2012	46.1
2003	35.8	2013	33.1
2004	40.2	2014	35.0
2005	41.2	2015	39.3
2006	39.8	2016	42.0
2007	39.7	2017	41.7
2008	40.5	2019	37.7
2009	42.5	2019	36.6

2. Annual precipitation measurements (Pi in cm) for M City, were given in Problem 1. Determine the magnitude of the 10-year precipitation depth if the data fit:

1. the normal distribution.
2. the Gumbel distribution.

How many times was the P10 (normal) exceeded in the 20-year annual precipitation record given in Problem 1 ?

Please clarify each step of the solution

Answer 1

For the given data of precipitation mean, standard deviation and skewness coefficient was calculated using the formula mentioned. After that to find 10-year precipitation using Normal distribution standard normal table was used. I have attached the normal table for reference.

Feedback appreciated!! Thanks!