Question

For a standard Normal random variable find the following probabilities. a. X is less than 1.72

b. X is less than -0.88

c. X is between 1.30 and 1.75

d. X is between -0.25 and 0.45

Answer 1

a. $P(Z<1.72)=0.9573.$

b. $P(Z<-0.88)=1-P(Z<0.88)=1-0.8106=0.1894.$

c. $P(1.30<Z<1.75)=P(Z<1.75)-P(Z<1.30)=0.9599-0.9032=0.0567.$

d. $P(-0.25<Z<0.45)=P(Z<0.45)-P(Z<-0.25)=$

$=P(Z<0.45)-[1-P(Z<0.25)]=0.6736-(1-0.5987)=0.2723.$