Question

 

Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)

(a) The area to the left of z is 0.2119.

(b) The area between −z and z is 0.9398.

(c) The area between −z and z is 0.2052.

(d) The area to the left of z is 0.9949.

(e) The area to the right of z is 0.5793.

Answer 1

Part a)

P ( Z < ? ) = 0.2119

Looking for the probability 0.2119 in standard normal table to calculate the critical value

Z = - 0.80

P ( Z < - 0.80 ) = 0.2119

Part b)

P ( a < Z < b ) = 0.9398

0.9398 / 2 = 0.4699

a = 0.5 - 0.4699 = 0.0301

b = 0.5 + 0.4699 = 0.9699

Looking for the probability 0.0301 and 0.9699   in standard normal table to calculate the critical value Z = -1.88 and Z = 1.88

P ( - 1.88 < Z < 1.88 ) = 0.9398

Part c)

P ( a < Z < b ) = 0.2052

0.2052/ 2 = 0.4699

a = 0.5 - 0.4699 = 0.3974

b = 0.5 + 0.4699 = 0.6026

Looking for the probability 0.3974 and 0.6026 in standard normal table to calculate the critical value Z = -0.26 and Z = 0.26

P ( - 0.26 < Z < 0.26 ) = 0.2052

Part d)

P ( Z < ? ) = 0.9949

Looking for the probability 0.9949 in standard normal table to calculate the critical value

Z = 2.57

P ( Z < 2.57 ) = 0.9949

part e)

P ( Z > ? ) = 0.5793

P ( Z < ? ) = 1 - P ( Z > ? ) = 1 - 0.5793 = 0.4207

Looking for the probability 0.4207 in standard normal table to calculate the critical value

Z = -0.20

P ( Z > -0.20 ) = 0.5793