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(-1.5 < Z < 0.69)? .6754 Correct: Your answer is correct. b. What is P(0 < Z < 1.47)? .4278 Correct: Your answer is correct. c. What is P(Z > -1.62)? .9525 Correct: Your answer is correct. d. What is P(Z < -2.57)? .0052 Correct: Your answer is correct. e. What is P(Z < 2.57)? .9955 Correct: Your answer is correct. f. What is P(-2.49 < Z < -1.22)?

Answer 1

a) P=0.6881

b) P=0.4292

c) P=0.9474

d) P=0.0051

e) P=0.9950

f) P=0.1048

Explanation:

a) What is P(-1.5 < Z < 0.69)?

`P(-1.5 < z < 0.69)=P(z<0.69)-P(z<-1.5)\\\\P(-1.5 < z < 0.69)=0.7549-0.0668=0.6881`

b) What is P(0 < Z < 1.47)?

`P(0 < z < 1.47)=P(z<1.47)-P(z<0)\\\\P(0 < z < 1.47)=0.9292-0.5=0.4292`

c) What is P(Z > -1.62)?

`P(z>-1.62)=0.9474`

d) What is P(Z < -2.57)?

`P(z<-2.57)=0.0051`

e) What is P(Z < 2.57)?

`P(z<2.57)=0.9950`

f) What is P(-2.49 < Z < -1.22)?

`P(-2.49 < Z < -1.22)=P(z<-1.22)-P(z<-2.49)\\\\P(-2.49 < Z < -1.22)=0.1112-0.0064=0.1048`