Chlorine concentration in a municipal water supply is a unif

Chlorine concentration in a municipal water supply is a uniformly distributed random variable that ranges between 0.75 ppm and 0.98 ppm

what is the mean chlorine concentration?

calculate standard deviation

What is the probability that the chlorine concentration will exceed 0.90 ppm on a given day

What is the probability that the chlorine concentration will be under 0.80 ppm?

What is the probability that the chlorine concentration will be between 0.80 ppm and 0.92 ppm?

Solution

a)

mean = (a+b)/2 = (0.98+0.75)/2 = 0.865

b)

standard deviation = sqrt[(a-b)^2/12] = sqrt((0.98-0.75)^2/12) = 0.066395281 [ANSWER]

c)

P(x>0.90) = (0.98-0.90)/(0.98-0.75) = 0.347826087 [ANSWER]

d)

P(x<0.80) = (0.80-0.75)/(0.98-0.75) = 0.217391304

e)

P(0.80<x<0.92) = (0.92-0.80)/(0.98-0.75) = 0.52173913