Use Appendix Table III to determine to 5 decimal places the following probabilities for the standard normal random variable Z: (a) P(Z < 1.31) ▪ (b) P(Z < 3.0)= i (c) P(Z > 1.45) = (d) P(Z > 2.15) = i (e) P(-2.34 < Z < 1.76)
Use Appendix Table III to determine to 5 decimal places the following probabilities for the standard normal random variable Z: (a) P(Z < 1.31) ▪ (b) P(Z < 3.0)= i (c) P(Z > 1.45) = (d) P(Z > 2.15) = i (e) P(-2.34 < Z < 1.76)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![### Standard Normal Distribution Probability Calculation
Use **Appendix Table III** to determine to 5 decimal places the following probabilities for the standard normal random variable \( Z \):
(a) \( P(Z < 1.31) \) = [Enter value]
(b) \( P(Z < 3.0) \) = [Enter value]
(c) \( P(Z > 1.45) \) = [Enter value]
(d) \( P(Z > -2.15) \) = [Enter value]
(e) \( P(-2.34 < Z < 1.76) \) = [Enter value]
### Instructions:
1. **Appendix Table III** refers to the Z-table which shows the cumulative probability of a standard normal distribution up to a given z-score.
2. Locate the z-score on the table to find its corresponding cumulative probability.
3. For values where \( Z > x \), use \( P(Z > x) = 1 - P(Z \le x) \).
4. For values within a range (e.g., \( a < Z < b \)), use \( P(a < Z < b) = P(Z \le b) - P(Z \le a) \).
\( \blacksquare \text{Ensure to find each probability to 5 decimal places.} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbb0b53a-c5e9-4f61-9041-8945e4ef01cb%2F2fe811d1-4729-4ce7-8ebd-bb8edd763edb%2F1c7nep9_processed.png&w=3840&q=75)
Transcribed Image Text:### Standard Normal Distribution Probability Calculation
Use **Appendix Table III** to determine to 5 decimal places the following probabilities for the standard normal random variable \( Z \):
(a) \( P(Z < 1.31) \) = [Enter value]
(b) \( P(Z < 3.0) \) = [Enter value]
(c) \( P(Z > 1.45) \) = [Enter value]
(d) \( P(Z > -2.15) \) = [Enter value]
(e) \( P(-2.34 < Z < 1.76) \) = [Enter value]
### Instructions:
1. **Appendix Table III** refers to the Z-table which shows the cumulative probability of a standard normal distribution up to a given z-score.
2. Locate the z-score on the table to find its corresponding cumulative probability.
3. For values where \( Z > x \), use \( P(Z > x) = 1 - P(Z \le x) \).
4. For values within a range (e.g., \( a < Z < b \)), use \( P(a < Z < b) = P(Z \le b) - P(Z \le a) \).
\( \blacksquare \text{Ensure to find each probability to 5 decimal places.} \)
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