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 ha: 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 1.6 1.8 2 4 Z 8 1.4 7

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j) What is the probability that the X, Y, and Z are all less than their respective 80th percentiles?
k) What is the probability that X + Z > 0?
Transcribed Image Text:j) What is the probability that the X, Y, and Z are all less than their respective 80th percentiles? k) What is the probability that X + Z > 0?
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
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
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