(b) What is P(X ≤ 0.7) [i.e., F(0.7)]? (Round your answer to four decimal places.) 0.1960 (c) Using the cdf from (a), what is P(0.45 < x≤ 0.7)? (Round your answer to four decimal places.) 0.1869 What is P(0.45 ≤ x ≤ 0.7)? (Round your answer to four decimal places.) 0.1869 (d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.) 7 0.4207 x (e) Compute E(X) and ox. (Round your answers to four decimal places.) E(X)= 0.8 0.1206 (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.) 10 0.1551 x
(b) What is P(X ≤ 0.7) [i.e., F(0.7)]? (Round your answer to four decimal places.) 0.1960 (c) Using the cdf from (a), what is P(0.45 < x≤ 0.7)? (Round your answer to four decimal places.) 0.1869 What is P(0.45 ≤ x ≤ 0.7)? (Round your answer to four decimal places.) 0.1869 (d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.) 7 0.4207 x (e) Compute E(X) and ox. (Round your answers to four decimal places.) E(X)= 0.8 0.1206 (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.) 10 0.1551 x
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 51E
Related questions
Question
![Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below.
P(x) = {72X² (1
2x7(1-x)
(a) Graph the pdf.
f(x)
4
3
O
f(x)
4)
3
2
Obtain the cdf of X.
1
Need Help?
F(x) =
Graph the cdf of X.
F(x)
1.0
0.8
O
0.6
0.4
0.2
F(x)
1.0
0.8
0.6
0.4
0.2
0.2
0.2
0
0 < x < 1
otherwise
1
8
-8x + 9x°
Read It
0.2
0.2
0.4
0.4
0.4
0.4
0.6
✓
0.6
x < 0
0≤x≤ 1
X> 1
0.6
0.6
0.8
0.8
0.8
0.8
1.0
1.0
1.0
1.0
X
X
X
X
f(x)
4
3
O
2
What is P(0.45 ≤ x ≤ 0.7)? (Round your answer to four decimal places.)
0.1869
✓
f(x)
4
3
(e) Compute E(X) and y. (Round your answers to four decimal places.)
E(X)=0.8
x=0.1206
2
O
✓
1
O
F(x)
1.0
(b) What is P(X ≤ 0.7) [i.e., F(0.7)]? (Round your answer to four decimal places.)
40.1960
0.2
O
X
F(x)
1.0
0.8
L
0.6
0.4
0.2
0.2
0.2
0.2
0.8
L
0.6
0.4
0.2
0.4
(c) Using the cdf from (a), what is P(0.45 < X ≤ 0.7)? (Round your answer to four decimal places.)
50.1869
<
0.4
0.4
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
70.4207
|x
0.4
0.6
0.6
0.6
0.8
0.6
0.8
0.8
0.8
1.0
1.0
1.0
1.0
X
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.)
10 0.1551
x
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F913a0921-d398-48e9-845b-58c3dce12c9b%2Fd9cb2bca-e88b-42dd-b090-acb3a21e53c7%2Fy1h6id_processed.png&w=3840&q=75)
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.
P(x) = {72X² (1
2x7(1-x)
(a) Graph the pdf.
f(x)
4
3
O
f(x)
4)
3
2
Obtain the cdf of X.
1
Need Help?
F(x) =
Graph the cdf of X.
F(x)
1.0
0.8
O
0.6
0.4
0.2
F(x)
1.0
0.8
0.6
0.4
0.2
0.2
0.2
0
0 < x < 1
otherwise
1
8
-8x + 9x°
Read It
0.2
0.2
0.4
0.4
0.4
0.4
0.6
✓
0.6
x < 0
0≤x≤ 1
X> 1
0.6
0.6
0.8
0.8
0.8
0.8
1.0
1.0
1.0
1.0
X
X
X
X
f(x)
4
3
O
2
What is P(0.45 ≤ x ≤ 0.7)? (Round your answer to four decimal places.)
0.1869
✓
f(x)
4
3
(e) Compute E(X) and y. (Round your answers to four decimal places.)
E(X)=0.8
x=0.1206
2
O
✓
1
O
F(x)
1.0
(b) What is P(X ≤ 0.7) [i.e., F(0.7)]? (Round your answer to four decimal places.)
40.1960
0.2
O
X
F(x)
1.0
0.8
L
0.6
0.4
0.2
0.2
0.2
0.2
0.8
L
0.6
0.4
0.2
0.4
(c) Using the cdf from (a), what is P(0.45 < X ≤ 0.7)? (Round your answer to four decimal places.)
50.1869
<
0.4
0.4
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
70.4207
|x
0.4
0.6
0.6
0.6
0.8
0.6
0.8
0.8
0.8
1.0
1.0
1.0
1.0
X
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.)
10 0.1551
x
X
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