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Water use in the summer is normally distributed with a mean of 300 million gallons per...

Water use in the summer is normally distributed with a mean of 300 million gallons per day and a standard deviation of 50 million gallons per day. City reservoirs have a combined storage capacity of 350 million gallons. If, P(X>x)=0.93 => P(Z<b) = a, what is the value of a? Here b would be standardized value from x.

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Answer #1

mean = 300 and sd = 50

0.93 represents 1.4758 value of z
hence b = 1.4758 and a = 0.93

now using central limit theorem,
x = 300 + 1.4758*50
x = 373.79

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