Question

Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.) (a) The area to the right of z is 0.08. (b) The area to the right of z is 0.025. (c) The area to the right of z is 0.05. (d) The area to the right of z is 0.10.

Answer 1

Answer:

Given that,

a)

P(z > z) = 0.08

1 - P (z  < z) = 0.08

P   (z  < z) = 1 - 0.08) = 0.92

P (z  < 1.41) = 0.92

z = 1.41

b)

P(z > z) = 0.025

1 - P (z  < z) = 0.025

P   (z  < z) = 1 - 0.025) = 0.975

P (z  < 1.96) = 0.975

z = 1.96

c)

P(z > z) = 0.05

1 - P (z  < z) = 0.05

P   (z  < z) = 1 - 0.05) = 0.95

P (z  < 1.65) = 0.95

z = 1.65

d)

P(z > z) = 0.10

1 - P (z  < z) = 0.10

P   (z  < z) = 1 - 0.10) = 0.9

P (z  < 1.28) = 0.9

z = 1.28