Question

Consider a random variable Z which has a standard normal distribution (mu = 0, sigma = 1). Choose which of the following values would be equivalent to the following probability:

P (Z > 0.54)
A. P(Z > 0.54.
B. P(Z < 0.54).
C. 1 - P(Z < - 0.54).
D. 1 - P(Z < 0.54).

Answer 1

A. P ( Z > 0.54) = 0,7054

B. P ( Z < 0.54) = 0.2946

C.1) 1 - 0.2946 = 0.7054

D.1) 1 - 0.2946 = 0.7054

Explanation:

A) P ( Z > 0.54) = 1 - P ( Z ≤ 0.54)

P ( Z ≤ 0.54) = 0,2946 from z-table

P ( Z > 0.54) = 1 - 0,2946

P ( Z > 0.54) = 0,7054

B) P ( Z < 0.54) = 0.2946

C) 1 - P ( Z < - 0,54)

1 - 0.2946 = 0.7054

D) 1 - P ( Z < 0,54)

1 - 0.2946 = 0.7054