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In: Statistics and Probability

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) =

56x⁶(1 − x)		0 < x < 1
0		otherwise

(a) Graph the pdf.

Obtain the cdf of X.

F(x) =

0	x < 0
	0 ≤ x ≤ 1
1	x > 1

Graph the cdf of X.

(b) What is P(X ≤ 0.65) [i.e., F(0.65)]? (Round your answer to four decimal places.)

(c) Using the cdf from (a), what is P(0.25 < X ≤ 0.65)? (Round your answer to four decimal places.)

What is P(0.25 ≤ X ≤ 0.65)? (Round your answer to four decimal places.)

(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)

(e) Compute E(X) and σ_X. (Round your answers to four decimal places.)

E(X)	=
σ_X	=

(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)

Expert Solution

orchestra answered 1 year ago

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

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