Question

Suppose T and Z are random variables. a. If Upper P left parenthesis Upper T greater than 2.33 right parenthesis equals0.05 and Upper P left parenthesis Upper T less than minus 2.33 right parenthesis equals0.05​, obtain Upper P left parenthesis negative 2.33 less than or equals Upper T less than or equals 2.33 right parenthesis . b. If Upper P left parenthesis negative 0.84 less than or equals Upper Z less than or equals 0.84 right parenthesis equals0.60 and also Upper P left parenthesis Upper Z greater than 0.84 right parenthesis equalsUpper P left parenthesis Upper Z less than minus 0.84 right parenthesis. Find Upper P left parenthesis Upper Z greater than 0.84 right parenthesis . a. Upper P left parenthesis negative 2.33 less than or equals Upper T less than or equals 2.33 right parenthesis equalsnothing

Answer 1

Solution :

a) Suppose T and Z are random variables.

Upper P left parenthesis Upper T greater than 2.33 right parenthesis equals0.05 and Upper P left parenthesis Upper T less than minus 2.33 right parenthesis equals0.05​, obtain Upper P left parenthesis negative 2.33 less than or equals Upper T less than or equals 2.33 right parenthesis.

So P(-2.33 T 2.33) = 0.90

b) Given :

If Upper P left parenthesis negative 0.84 less than or equals Upper Z less than or equals 0.84 right parenthesis equals0.60 and also Upper P left parenthesis Upper Z greater than 0.84 right parenthesis equalsUpper P left parenthesis Upper Z less than minus 0.84 right parenthesis.

P (-0.84 Z 0.84) = 0.60

P(Z>0.84) + P(-0.84 Z 0.84) + P(Z<-0.84) = 1

P(Z>0.84) + 0.60 +P(Z>0.84)= 1

P(Z<-0.84)=P(Z>0.84)]

2×P(Z>0.84) = 1 - 0.60

2×P(Z>0.84) = 0.40

P(Z>0.84) = 0.40/2

P(Z>0.84) = 0.20

Therefore

a) Upper P left parenthesis negative 2.33 less than or equals Upper T less than or equals 2.33 right parenthesis equals 0.90

b) Upper P left parenthesis Upper Z greater than 0.84 right parenthesis is 0.20