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If Z is N(0, 1), find

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 2E Chapter 3.3

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 2E

If \(Z\) is \(N(0,1)\), find

(a) \(P(0 \leq Z \leq 0.87)\).

(b) \(P(-2.64 \leq Z \leq 0)\).

(c) \(P(-2.13 \leq Z \leq-0.56)\).

(d) \(P(|Z|>1.39)\).

(e) \(P(Z<-1.62)\).

(f) \(P(|Z|>1)\).

(g) \(P(|Z|>2)\).

(h) \(P(|Z|>3)\).

Equation Transcription:


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Text Transcription:

Z  

N(0,1)  

P(0 < or = Z < or = 0.87)

P(−2.64 < or = Z < or = 0)

P(−2.13 < or = Z < or =−0.56)

P(|Z|>1.39) . P(Z<−1.62).

P(|Z|>1)

P(|Z|>2)

P(|Z|>3)

Step-by-Step Solution:

Solution :

Step 1 of 3:

If Z is the standard normal distribution  N(0,1). We have to find the probabilities.

  1. P(0<Z0.87)
  2. P(-2.64Z<0)
  3. P()
  4. P(|Z|>1.39)
  5. P(Z <-1.62)
  6. P(|Z|>1)
  7. P(|Z|>2)
  8. P((|Z|>3).

Step 2 of 3

Chapter 3.3, Problem 2E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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If Z is N(0, 1), find