Suppose T and Z are random variables. a. If Upper P left parenthesis Upper T greater than 2.57 right parenthesisequals0.04 and Upper P left parenthesis Upper T less than minus 2.57 right parenthesisequals0.04, obtain Upper P left parenthesis negative 2.57 less than or equals Upper T less than or equals 2.57 right parenthesis. b. If Upper P left parenthesis negative 0.36 less than or equals Upper Z less than or equals 0.36 right parenthesisequals0.28 and also Upper P left parenthesis Upper Z greater than 0.36 right parenthesisequalsUpper P left parenthesis Upper Z less than minus 0.36 right parenthesis. Find Upper P left parenthesis Upper Z greater than 0.36 right parenthesis.
Answer a)
Given,
P(T>2.57) = 0.04 and P(T<-2.57) = 0.04
P(T>2.57) + P(-2.57<= T <=2.57) + P(T<-2.57) = 1
0.04 + P(-2.57<= T <=2.57) + 0.04 = 1
P(-2.57<= T <=2.57) = 1 - 0.04 - 0.04
P(-2.57<= T <=2.57) = 0.92
Answer b)
Given,
P (-0.36 <= Z <= 0.36) = 0.28
P(Z>0.36) + P(-0.36<= Z <=0.36) + P(Z<-0.36) = 1
P(Z>0.36) + 0.28 + P(Z<-0.36) = 1
Also, P(Z>0.36) = P(Z<-0.36)
2*P(Z>0.36) = 1 - 0.28
2*P(Z>0.36) = 0.72
P(Z>0.36) = 0.72/2
P(Z>0.36) = 0.36
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