Question

Given the standard normal random variable Z, answer the following questions.

a. What is the probability that Z is between 1.35 and 1.85?

b. If P(-z<Z<z)=88%, what is z?

c. What is the probability that Z is less than -0.55 or greater than 1.20?

Answer 1

Solution,

a) Using standard normal table,  

P( 1.35 < Z < 1.85)

= P( Z < 1.85) - P( Z < 1.35)

= 0.9678 - 0.9115

= 0.0563

b) Using standard normal table,

P( -z < Z < z) = 88%

= P(Z < z) - P(Z <-z ) = 0.88

= 2P(Z < z) - 1 = 0.88

= 2P(Z < z) = 1 + 0.88

= P(Z < z) = 1.88 / 2

= P(Z < z) = 0.94

= P(Z < 1.55 ) = 0.94

= z  ± 1.55

c) Using standard normal table

P( Z < -0.55 OR Z > 1.20 )

= P(Z < -0.55 ) + P( Z > 1.20 )

= 0.2912 + 1 - P(Z < 1.20)

= 0.2912 + 1 - 0.8849

= 0.2912 + 0.1151

= 0.4063