Sec_3_solutions_07 - CEE 304 Section 3 Solutions 1 Suppose...

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CEE 304 – Section 3 Solutions 1. Suppose the concentrations of a reagent in samples generated in a laboratory are normally distributed. You are told that the reagent concentration must be within 3.0 ± 0.01 mg/l. No concentration outside this range is acceptable. You know from experience that reagent concentrations have μ = 3.0 mg/l and σ = 0.005 mg/l. a.) On average, how many samples will be discarded? Ans. 4.56% b.) How many samples fall within ± 1 standard deviation of the mean? Ans. 68.3% c.) What reagent concentrations delineate the 95 th and 5 th percentile? Ans. X 0.95 = 3.0082, X 0.05 = 2.9918 2. Suppose the weekly demand for propane gas (in thousands of gallons) is a random variable X with pdf: 2 1 ( ) 2 1 f x x = - for 1 x 2, and 0 otherwise a.) Show that it is a pdf. Ans. First must check if f ( x ) is defined for all x , which it is! Second, check if f ( x ) 0 for all x , which it is! Third, check if 2 1 ( ) 2 1 1 f x dx dx x + + - - = - = , which it does!
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