STAT312.ICE04.pdf - Stat-312 ICE#04 Continuous Probability...

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Stat-312: ICE #04 Continuous Probability Distributions Name: 1. A random number generator is used to produce values between 10 and 20, e.g ., X = 10*rand() + 10 . (a) Sketch the Probability Density Function (PDF) and Cumulative Distribution Function (CDF) for the random variable X produced by this process. (b) What is the probability that this process will produce a value of exactly 15.0? P( X = 15) = (c) What is the probability that this process will produce a value between 10.0 and 12.0? P(10.0 < X 12.0) = 2. Manufacturing a rod, with length specification of 5.0±0.1 cm, the following length measurements were made on a sample of parts from the production line: 5.000 4.962 4.981 5.011 4.949 4.960 4.955 5.032 4.983 4.969 5.058 5.031 5.019 4.998 4.989 4.993 (a) Calculate the following statistics for the “length” sample data listed above: n x = S x (sample st. dev.) = 0.03112314 Q 1 = IQR = median = Q 3 = (b) What proportion of Sample Parts are out of spec? Proportion of failing parts in the Sample = (c) What is the Process Capability Index? = x x p S x USL , S LSL x min c k 3 3 = (d) Assume that the complete

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