Question

Find the probabilities that a random variable having the standard normal distribution will take on a value (a) between 0.87 and 1.20; (b) between -0.34 and 0.60; (c) greater than 0.85; (d) greater than -0.60.

Answer 1

solution

(A)P( 0.87< Z <1.20 )

= P(Z <1.20 ) - P(Z <0.87 )

Using z table,  

=0.8849-0.8078   

probability=0.0771

(B)

P( -0.34< Z <0.60 )

= P(Z <0.60 ) - P(Z <-0.34 )

Using z table,  

=0.7257-0.3669

probability=0.3588

(C)

P(z > 0.85) =1 - P(z <0.85 )

Using z table,
= 1 -0.8023

= 0.1977

probability= 0.1977   

(D)

P(z >-0.60) =1 - P(z <-0.60)

Using z table,
= 1 -0.2743

= 0.7257

probability= 0.7257