Question

Suppose Z denotes the standard normal random variable. Compute the following

a) P (Z > 2)

b) P(-1 < Z < 2.31)

c) P (1.21 < Z < 2.42)

d) P (Z < 1.37)

e) P (Z > -1)

Show working

Answer 1

We can compute the probabilities using any software or standard normal tables. We would be using R here as:

a) P(Z > 2) = 1 - P(Z < 2)

Therefore 0.02275013 is the required probability here.

b) The probability here is computed as:
P( -1 < Z < 2.31) = P(Z < 2.31) - P(Z < -1)

Therefore 0.8309007 is the required probability here.

c) The probability here is computed as:
P( 1.21 < Z < 2.42) = P(Z < 2.42) - P(Z < 1.21)

Therefore 0.1053792 is the required probability here.

d) The probability here is computed as:
P(Z < 1.37)

Therefore 0.9146565 is the required probability here

e) The probability here is computed as:
P( Z > -1) = 1 - P(Z < -1)

Therefore 0.8413447 is the required probability here.