Question

Assume z is a standard normal random variable. Compute the following probabilities.

a. P(–1.33 ≤ z ≤ 1.67)

b. P(1.23 ≤ z ≤ 1.55)

c. P(z ≥ 2.32)

d. P(z ≥ –2.08)

 e. P(z ≥ –1.08)

Answer 1

a)

P ( - 1.33 < Z < 1.67 ) = P ( Z < 1.67 ) - P ( Z < - 1.33 )

By Using Standard Normal Table,

P ( - 1.33 < Z < 1.67 ) = 0.9525 - 0.0918

P ( - 1.33 < Z < 1.67 ) = 0.8607

b)

P ( 1.23 < Z < 1.55 ) = P ( Z < 1.55 ) - P ( Z < 1.23 )

By Using Standard Normal Table,

P ( 1.23 < Z < 1.55 ) = 0.9394 - 0.8907

P ( 1.23 < Z < 1.55 ) = 0.0487

c)

P ( Z > 2.32 ) = 1 - P ( Z < 2.32 )

By Using Standard Normal Table,

P ( Z > 2.32 ) = 1 - 0.9898

P ( Z > 2.32 ) = 0.0102

d)

By Using Standard Normal Table,

P ( Z < - 2.08 ) = 0.0188

e)

By Using Standard Normal Table,

P ( Z < - 1.08 ) = 0.1401