Question

Answer the following questions about the standard normal random variable Z. (Use 4 decimal places in your answers to parts a. through f.)

a. What is P(-1.55 < Z < 0.61)?

b. What is P(0 < Z < 1.33)?

c. What is P(Z > -1.72)?

d. What is P(Z < -2.7)?

e. What is P(Z < 2.63)?

f. What is P(-2.57 < Z < -1.22)?

Answer 1

BY USING STANDARD NORMAL TABLE WE HAVE

SOLUTION A: P(a ≤ Z ≤ b) = P(Z ≤ b) – P(Z ≤ a)

P(-1.55 < Z < 0.61)= P(Z < 0.61)-P(Z)=0.27093-0.060571=  0.6685

SOLUTION B: P(0<Z<1.33) = P(Z)-P(Z < 1.33) =  0.5-0.091759=0.4082

SOLUTION C:P(Z > -1.72)=  1-P(Z=-1.72)=

SOLUTION D:P(Z < -2.7)=0.0035

SOLUTION E:P(Z < 2.63)= 0.9957

SOLUTION F:P(-2.57 < Z < -1.22)= P(-2.57<Z<-1.22) = P(Z=-1.22)-P(Z=-2.57)=