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Chapter 5: Q 5.124 (page 226)

Suppose that T and Z are random variables.

(a) If P(T>2.02)=0.05and P(T<-2.02)=0.05,determine P(-2.02鈮�T鈮�2.02)

(b) Suppose that P(-1.64鈮�Z鈮�1.64)=0.90and suppose that P(Z>1.64)=P(Z<-1.64).

FindP(Z>1.64).

Short Answer

Expert verified

Part (a) P(-2.02鈮�T鈮�2.02)=0.9.

Part (b)P(Z>1.64)=0.05.

Step by step solution

01

Part (a) Step 1. Given information

P(T>2.02)=0.05andP(T<-2.02)=0.05

02

Part (a) Step 2. Solution

P(-2.02鈮�T鈮�2.02)=1-[P(T>2.02)=0.05+P(T<-2.02)]=1-(0.05+0.05)=1-0.1=0.9

03

Part (b) Step 1. Given information 

P(Z>1.64)=P(Z<-1.64)andP(-1.64鈮�Z鈮�1.64)=0.90

04

Part (b) Step 2. Solution.

P(Z>1.64)=1-[P(-1.64鈮�Z鈮�1.64)+P(Z<-1.64]P(Z>1.64)=1-[0.90+P(Z>1.64)]2路P(Z>1.64)=0.10P(Z>1.64)=0.05

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Most popular questions from this chapter

In each of Exercises 5.167-5.172, we have provided the number of trials and success probability for Bernoulli trials. LetX denote the total number of successes. Determine the required probabilities by using

(a) the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places.

(b) TableVII in AppendixA. Compare your answer here to that in part (a).

n=3,p=0.4,P(X=1)

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In each of Exercises 5.167-5.172, we have provided the number of trials and success probability for Bernoulli trials. LetX denote the total number of successes. Determine the required probabilities by using

(a) the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places.

(b) TableVII in AppendixA. Compare your answer here to that in part (a).

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