authors studied the impact of several factors involving the heat treatment of le

Question

authors studied the impact of several factors involving the heat treatment of leaf springs. In this process, a conveyor system transports leaf spring assemblies through a high temperature furnace. After the spring leaves a high pressure press, an oil quench cools it to near room temperature . An important material property of this process is the resulting free height of the spring, which should ideally be 8 inches. A materials engineer assigned to this process believes that the heating time affects this free height and so carries out 25 tests at two different times - 23 seconds and 25 seconds. The results are shown here: Spring free height at: 23 seconds 25 seconds 7.12 7.33 7.33 7.54 7.34 7.77 7.37 8.07 7.45 8.1 7.47 8.14 7.51        8.23 7.51        8.26 7.52        8.27 7.53        8.31 7.56        8.31 7.57        8.36 7.57     8.36 7.61        8.36 7.65        8.37 7.66     8.37 7.67        8.39 7.67        8.42 7.67        8.42 7.67     8.45 7.71        8.45 7.71        8.46 7.71        8.48 7.71        8.49 7.75        8.53
Spring free height at: 23 seconds 25 seconds 7.12 7.33 7.33 7.54 7.34 7.77 7.37 8.07 7.45 8.1 7.47 8.14 7.51        8.23 7.51        8.26 7.52        8.27 7.53        8.31 7.56        8.31 7.57        8.36 7.57     8.36 7.61        8.36 7.65        8.37 7.66     8.37 7.67        8.39 7.67        8.42 7.67        8.42 7.67     8.45 7.71        8.45 7.71        8.46 7.71        8.48 7.71        8.49 7.75        8.53 Spring free height at: 23 seconds 25 seconds 7.12 7.33 7.33 7.54 7.34 7.77 7.37 8.07 7.45 8.1 7.47 8.14 7.51        8.23 7.51        8.26 7.52        8.27 7.53        8.31 7.56        8.31 7.57        8.36 7.57     8.36 7.61        8.36 7.65        8.37 7.66     8.37 7.67        8.39 7.67        8.42 7.67        8.42 7.67     8.45 7.71        8.45 7.71        8.46 7.71        8.48 7.71        8.49 7.75        8.53
QUESTION 1 You have obtained 0.44 as a random number between 0 and 1 (using Excel's Rando function). Convert this into a random draw and b-40 from a triangular distribution with additional parameter c-35 (where the triangle peaks). # 15 Provide your answer to 2 decimal places

Explanation / Answer

Here this random number 0.44 will be used as the cumulative distribution where a = 15 and b = 40 and c = 35

so let say the random draw is X

so Pr(x < X ; 15;35; 40) = 0.44

for a triangular distribution. the cumulative distribution is

F(x) = (x -a)2 / (b-a)(c-a) which is equal to 0.44

0.44 = (x - 15)2 / (25 * 20)

(x - 15)2  = 0.44 * 25 *20 = 220

(x -15) = 14.83

x = 14.83 + 15 = 29.83

we converted that random number into a random draw of x= 29.83

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