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Section 3

# Section 3 - CEE 304 Section 3 Problems Fall 08 1 Suppose a...

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CEE 304 – Section 3 Problems Fall 08 1. Suppose a buffering solution with a concentration of 3.0 ± 0.01 mg/L of ball bearings are normally distributed. You are told that the concentration of a buffering solution must be within 3.0 ± 0.01 mg/L. No concentration outside this range is acceptable. You know from practice that concentrations have μ = 3.0 mg/L and σ = 0.005 mg/L. a.) On average, how many buffering solutions will be unacceptable? Ans. 4.56% b.) How many buffering solution concentrations fall within ± 1 standard deviation of the mean? Ans. 68.3% c.) What 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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Section 3 - CEE 304 Section 3 Problems Fall 08 1 Suppose a...

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