Maintaining a constant pipe wall temperature in some hotprocess applications is

Question

Maintaining a constant pipe wall temperature in some hotprocess applications is critical. A new technique that utilizes bolton trace elements to maintain temperature was presented in a scientific journal. Without bolton trace elements, the pipe wall temperature of a switch condenser used to produce plastic has a uniform distribution ranging from 256F to 288 . When several bolton trace elements are attached to the piping, the wall temperature is uniform from 278F to 285F Answer an integer or decimal rounded to four decimal places as needed. Ideally, the pipe wall temperature should range between 283F to 285F. What is the probability that the temperature will fall in this ideal range when no bolton trace elements are used? Submit Answer Tries 0/5 Submit Answer Tries 0/5 Submit Answer Tries 0/5 Submit Answar Tries 0/s The probability that the temperature will fall in the ideal range (between 283F to 285F) when bolton trace elements are attached to the pipe is When the temperature is 276F or lower, the hot liquid plastic hardens (or plates), causing a buildup in the piping. What is the probability of plastic plating when no bolton trace elements are used? When the temperature is 276F or lower, the hot liquid plastic hardens (or plates), causing a buidup in the piping. The probability of plastic plating when bolton trace elements are attached to the pipe is:

Explanation / Answer

Here if the bolten trace element temperature is x and no bolten trace element temerature is y.

f(x) = 1/(288 - 256) = 1/32 ; 256 < x < 288

F(x) = (x - 256)/32 ; 256 < x < 288

f(y) = 1/(285 - 278) = 1/7 ; 278 < y < 285

F(y) = (y - 278)/7 ; 278 < y < 285

(a) Pr(283 < x < 285) = F(285) - F(283) = 1/32 [(285 - 256) - (283 - 256)] = 1/16

(b) P(283 < y < 285) = F(285) - F(283) = 1/7 [(285 - 278) - (283 - 278)] = 2/7

(c) P(x < 276) = F(276) = (276 - 256)/32 = 20/32 = 5/8

(d) P(y < 276) = F(276) = 0

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