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 0.62 ppm and 0.96 ppm.

(Round to 4 decimal places).

(a)  

What is the mean chlorine concentration?

(b)  

Calculate the standard deviation?

(c)  

What is the probability that the chlorine concentration will exceed 0.82 ppm on a given day?

(d)  

What is the probability that the chlorine concentration will be under 0.77 ppm?

(e)  

What is the probability that the chlorine concentration will be between 0.80 ppm and 0.95 ppm?

Solution

a)

Mean = (a+b)/2 = (0.96+0.62)/2 = 0.79 [ANSWER]

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b)

standard deviation = sqrt[(a-b)^2/12] = sqrt((0.96-0.62)^2/12) = 0.098149546 [ANSWER]

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c)

Here, we treat the upper bound to be 0.96. Thus,

P(x>0.82) = (0.96-0.82)/(0.96-0.62) = 0.411764706 [ANSWER]

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d)

Here, we treat the lower bound to be 0.62. Thus,

P(x>0.82) = (0.77-0.62)/(0.96-0.62) = 0.441176471 [ANSWER]

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e)

P(0.80<x<0.95) = (0.95-0.80)/(0.96-0.62) = 0.441176471 [ANSWER]