Question

Determine the value of z* such that it satisfies the conditions below. (Assume that the requested value of z* is positive. Round your answers to two decimal places.)

(a) −z* and z* separate the middle 95% of all z values from the most extreme 5%. z* = 1.96 Correct: Your answer is correct.

(b) −z* and z* separate the middle 90% of all z values from the most extreme 10%. z* = 1.65 Correct: Your answer is correct.

(c) −z* and z* separate the middle 97.8% of all z values from the most extreme 2.2%. z* = 0.84 :

(d) −z* and z* separate the middle 82% of all z values from the most extreme 18%. z* =

Answer 1

Solution:

d)

Given that,

P( -z^* < Z < z ^*) = 0.84

P( Z < z^* ) - P( Z < -z^* ) = 0.84

2*P(Z < z^* ) - 1 = 0.84

2*P(Z < z^* ) = 1 + 0.84

P( Z < z ^*) = 1.84 / 2

P( Z < z^* ) = 0.92

P( Z < 1.41 ) = 0.92

z^* = 1.41