Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below. 56x6 (1x) 0 < x < 1 f(x) = {50x11 (a) Graph the pdf. otherwise f(x) 4 3 2 f(x) 4 3 2 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 Obtain the cdf of X. F(x) = 0 8x7-78 X < 0 0 ≤ x ≤ 1 Graph the cdf of X. F(x) 1.0 0.8 0.6 0.4 0.2 F(x) 1.0 0.8 0.6 0.4 20 0.2 1 x > 1 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 f(x) 4 3 2 1 f(x) 4 3 2 1 F(x) 1.0 0.8 0.6 0.4 0.2 F(X) 1.0 0.8 0.6 0.4 0.2 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 X 0.2 0.4 0.6 0.8 1.0 X 0.2 0.4 0.6 0.8 1.0 (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(0.35 < x < 0.65)? (Round your answer to four decimal places.) What is P(0.35 ≤ 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 σx. (Round your answers to four decimal places.) E(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.)
Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below. 56x6 (1x) 0 < x < 1 f(x) = {50x11 (a) Graph the pdf. otherwise f(x) 4 3 2 f(x) 4 3 2 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 Obtain the cdf of X. F(x) = 0 8x7-78 X < 0 0 ≤ x ≤ 1 Graph the cdf of X. F(x) 1.0 0.8 0.6 0.4 0.2 F(x) 1.0 0.8 0.6 0.4 20 0.2 1 x > 1 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 f(x) 4 3 2 1 f(x) 4 3 2 1 F(x) 1.0 0.8 0.6 0.4 0.2 F(X) 1.0 0.8 0.6 0.4 0.2 x 0.2 0.4 0.6 0.8 1.0 x 0.2 0.4 0.6 0.8 1.0 X 0.2 0.4 0.6 0.8 1.0 X 0.2 0.4 0.6 0.8 1.0 (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(0.35 < x < 0.65)? (Round your answer to four decimal places.) What is P(0.35 ≤ 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 σx. (Round your answers to four decimal places.) E(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.)
Chapter3: Polynomial Functions
Section3.2: Polynomial Functions Of Higher Degree
Problem 4ECP
Related questions
Question
Transcribed Image Text:Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below.
56x6 (1x) 0 < x < 1
f(x)
= {50x11
(a) Graph the pdf.
otherwise
f(x)
4
3
2
f(x)
4
3
2
x
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
Obtain the cdf of X.
F(x)
=
0
8x7-78
X < 0
0 ≤ x ≤ 1
Graph the cdf of X.
F(x)
1.0
0.8
0.6
0.4
0.2
F(x)
1.0
0.8
0.6
0.4
20
0.2
1
x > 1
x
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
f(x)
4
3
2
1
f(x)
4
3
2
1
F(x)
1.0
0.8
0.6
0.4
0.2
F(X)
1.0
0.8
0.6
0.4
0.2
x
0.2
0.4
0.6
0.8
1.0
x
0.2
0.4
0.6
0.8
1.0
X
0.2
0.4
0.6
0.8
1.0
X
0.2
0.4
0.6
0.8
1.0
![(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(0.35 < x < 0.65)? (Round your answer to four decimal places.)
What is P(0.35 ≤ 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 σx. (Round your answers to four decimal places.)
E(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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb898cad9-5347-4e0a-a74d-32f84bfad0f6%2F610f27c7-5ff8-4b89-80ff-55773c2996c3%2F6qiruhzs_processed.png&w=3840&q=75)
Transcribed Image Text:(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(0.35 < x < 0.65)? (Round your answer to four decimal places.)
What is P(0.35 ≤ 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 σx. (Round your answers to four decimal places.)
E(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.)
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