Question

For a standard normal? distribution, determine the probabilities in parts a through d below.

a. Find ?P(z ? 1.53).

b. Find ?P(z ? ?1.25?).

c. Find P(?0.81 ? z ? 1.77?).

d. Find ?P(0.33 ? z ? 2.11?).

Answer 1

Solution:

Given that,

Using standard normla table

, a ) ?P(z ? 1.53).
To see the z value 0.1 in the column and 0.53 in the row of the standard normal table the corresponding probability is
Probability =0.9370

b ) P(Z < - 1.25 )  
To see the z value - 0.1 in the column and 0.25 in the row of the standard normal table the corresponding probability is
Probability =0.1056

c ) P(?0.81 ? z ? 1.77?)

P ( z < 1.77 ) - P ( z < - 0.81 )

= 0.9616 - 0.2090

= 0.7526

Probability = 0.7526

d ) P(0.33 ? z ? 2.11 )

P ( z < 2.11 ) - P ( z < 0.33 )

= 0.9826 - 0.6293

= 0.3533

Probability = 0.3533