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Chapter 4: Q88E (page 262)

Find a value of the standard normal random variable z, call itz0 such that

a.P(-z0鈮�z鈮�z0)=.98b.P(z鈮�z0)=.05c.P(z鈮�z0)=.70d.P(z鈮�z0)=.025e.P(z鈮�z0)=.70

Short Answer

Expert verified

a.z0=2.326b.z0=1.645c.z0=-0.524d.z0=1.96e.z0=0.524

Step by step solution

01

Given information

z is a standard normal variable, which is calledz0.

02

Finding the value of z0 when P(-z0≤z≤z0)=.98 

a.P-z0鈮�z鈮�z0=0.982P0鈮�z鈮�z0=0.98DuetosymmetricdistrubutionP0鈮�z鈮�z0=0.49Pz鈮�z0-Pz<0=0.49Pz鈮�z0-0.50=0.49Pz鈮�z0=0.99桅z0=0.99z0=桅-10.99z0=2.326

Therefore, the z0the score is 2.326.

03

Finding the value of z0 when P(z≥z0)=.05

b.

Pz鈮�z0=0.051-Pz<z0=0.05Pz<z0=0.95桅z0=0.95z0=桅-10.95z0=1.645

Therefore, the z0 score is 1.645.

04

Finding the value of z0 when P(z≥z0)=.70

c.

Pz鈮�z0=0.701-Pz鈮�z0=0.70Pz鈮�z0=0.30

Therefore, the score is -0.524.

05

Finding the value of z0 when P(z≥z0)=.70

d.Pz鈮�z0=0.0251-Pz<z0=0.025Pz<z0=0.975桅z0=0.975z0=桅-10.975z0=1.96

Therefore, the z0 score is 1.96.

06

Finding the value z0 of when P(z≤z0)=.70

e.Pz鈮�z0=0.70桅z0=0.70z0=桅-10.70z0=0.524

Therefore, the z0 score is 0.524.

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