Let X denote the amount of space occupied by an article placed in a 1-ft3 packing...

Let X denote the amount of space occupied by an article placed in a 1-ft3 packing container. The pdf of X is below. f(x) = 42x5(1 − x) 0 < x < 1 0 otherwise (a) Graph the pdf. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Obtain the cdf of X. F(x) = 0 x < 0 Correct: Your answer is correct. 0 ≤ x ≤ 1 1 x > 1 Graph the cdf of X. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (b) What is P(X ≤ 0.6) [i.e., F(0.6)]? (Round your answer to four decimal places.) 0.1586 Correct: Your answer is correct. (c) Using the cdf from (a), what is P(0.3 < X ≤ 0.6)? (Round your answer to four decimal places.) 0.1548 Correct: Your answer is correct. What is P(0.3 ≤ X ≤ 0.6)? (Round your answer to four decimal places.) (d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.) 0.1063 Incorrect: Your answer is incorrect. (e) Compute E(X) and σX. (Round your answers to four decimal places.) E(X) = σX = (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)

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