g) What is the probability that T is < 5? h) What is the probability that 5
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Question
![Suppose X, Y, and Z are three independent normal random variables. X has an expected value of -7 and a standard deviation of 1.6; Y has an
expected value of -9 and a standard deviation of 1.8; Z has an expected value of 8 and a standard deviation of 1.4 Let T = 2X + 4Y+7Z
Variable
Mean(Expected Value)
Standard Deviation
Coefficient
X
Y
-7 -9
1.8
4
1.6
2
Z
8
1.4
7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62b236b3-1e1c-48f8-a6f5-9c3f49a681da%2Fd1e25dbb-93b2-431f-82f1-92e2ba439319%2Fym15gk_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose X, Y, and Z are three independent normal random variables. X has an expected value of -7 and a standard deviation of 1.6; Y has an
expected value of -9 and a standard deviation of 1.8; Z has an expected value of 8 and a standard deviation of 1.4 Let T = 2X + 4Y+7Z
Variable
Mean(Expected Value)
Standard Deviation
Coefficient
X
Y
-7 -9
1.8
4
1.6
2
Z
8
1.4
7
![g) What is the probability that T is < 5?
h) What is the probability that 5 <T < 7?
i) What is the 92nd percentile of the distribution of T?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62b236b3-1e1c-48f8-a6f5-9c3f49a681da%2Fd1e25dbb-93b2-431f-82f1-92e2ba439319%2Flo20qne_processed.png&w=3840&q=75)
Transcribed Image Text:g) What is the probability that T is < 5?
h) What is the probability that 5 <T < 7?
i) What is the 92nd percentile of the distribution of T?
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