There is 20 million m³ of water in a lake at the beginning of a month. Rainfall in this month is a random variable with an average of 1 million m³ and a standard deviation of 0.5 million m³. The monthly water flow entering the lake is also a random variable, with an average of 8 million m³ and a standard deviation of 2 million m³. Average monthly evaporation is 3 million m³ and standard deviation is 1 million m³. 10 million m³ of water will be drawn from the lake this month. a Calculate the mean and standard deviation of the water volume in the lake at the end of the month. b Assuming that all random variables in the problem are normally distributed, calculate the probability that the end-of-month volume will remain greater than 18 million m³.
