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Chapter 4: Q165S (page 281)

Find the following probabilities for the standard normal

random variable z:

a.P(z≤2.1)

b.P(z≥2.1)

c.P(z≥-1.65)

d.P(-2.13≤z≤-.41)

e.P(-1.45≤z≤2.15)

f.P(z≤-1.43)

Short Answer

Expert verified

a. P(z≤2.1)=0.9821

b. P(z≥2.1)=0.0179.

c. P(z≥-1.65)=0.9505

d..P(-2.13≤z≤-.41)=0.3243

e.P(-1.45≤z≤2.15)=0.9107

f. P(z≤-1.43)=0.0764

Step by step solution

01

Given information

Z is a standard normal random variable.

02

Calculate P(z≤2.1)

a.

In case of the standard normal random variable z, we can find probability Pz≤2.1as follows:

Pz≤21=0.9821

Hence, Pz≤21=0.9821.

03

Calculate P(z≥2.1)

b.

In case of the standard normal random variable z, we can find probabilityPz≤-1.43 as follows:

Pz≤-1.43=1-Pz≤-1.43=1-0.9236=0.0764

Hence,Pz≤2.1-0.0179 .

04

Calculate P(z≥-1.65)

c.

WhenPz≥-1.65,

Pz≥-1.65=Pz≥-1.65=0.9505

Hence, Pz≥-1.65=0.9505.

05

Calculate P(-2.13≤z≤-.41)

d.

P(-2.13≤z≤-.41)=Pz≤-.41-Pz≤-2.13=1-Pz≤-.41-1+Pz≤2.13=1-0.6591-1+0.9834=0.3243

Hence,P(-2.13≤z≤-.41)=0.3243.

06

Calculate P(-1.45≤z≤2.15)

e.

P-1.45≤2.15=Pz≤2.15-Pz≤-1.15=Pz≤2.15-1+Pz≤1.15=0.9842-1+0.9265=0.9107

Hence, P-1.45≤z≤2.15=0.9107.

07

Calculate P(z≤-1.43)

f.

Pz≤-1.43=1-Pz≤1.43=1-0.9236=0.0764

Hence, Pz≤-1.43=0.0764.

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