Find the following probability for the standard normal random variable z. e. P(-1szs1) f. P(-2 1) ..... a. P(z = 1) = 0 (Round to three decimal places as needed.) b. P(zs1) = .841 (Round to three decimal places as needed.) c. P(z< 1) = .841 (Round to three decimal places as needed.) d. P(z> 1) = (Round to three decimal places as needed.)
Find the following probability for the standard normal random variable z. e. P(-1szs1) f. P(-2 1) ..... a. P(z = 1) = 0 (Round to three decimal places as needed.) b. P(zs1) = .841 (Round to three decimal places as needed.) c. P(z< 1) = .841 (Round to three decimal places as needed.) d. P(z> 1) = (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Finding Probabilities for the Standard Normal Random Variable (z)**
Consider the following probabilities for the standard normal random variable \( z \):
1. **\( P(z = 1) \)**
- Probability calculation: \( 0 \)
- Notes: Round to three decimal places as needed.
2. **\( P(z \leq 1) \)**
- Probability calculation: \( 0.841 \)
- Notes: Round to three decimal places as needed.
3. **\( P(z < 1) \)**
- Probability calculation: \( 0.841 \)
- Notes: Round to three decimal places as needed.
4. **\( P(z > 1) \)**
- Probability calculation: [Requires calculation]
5. **\( P(-1 \leq z \leq 1) \)**
- Notes: Represents the probability that \( z \) falls within 1 standard deviation from the mean.
6. **\( P(-2 \leq z \leq 2) \)**
- Notes: Represents the probability that \( z \) falls within 2 standard deviations from the mean.
7. **\( P(-2.94 \leq z \leq 0.31) \)**
- Notes: Calculate probability for specific range.
8. **\( P(-0.04 < z < 1.89) \)**
- Notes: Calculate probability for specific range.
**Instructions:**
- When probability values are calculated, ensure they are rounded to three decimal places for consistency.
- These probabilities are derived from the standard normal distribution which is symmetric around a mean of 0 with a standard deviation of 1.
- Make use of z-tables or statistical software to find these probabilities accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40766f6b-1d39-4de4-8cc4-4220165d991f%2F26d3cc90-df8e-4693-83c1-074d3fd3c93d%2Fbmvpu9l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding Probabilities for the Standard Normal Random Variable (z)**
Consider the following probabilities for the standard normal random variable \( z \):
1. **\( P(z = 1) \)**
- Probability calculation: \( 0 \)
- Notes: Round to three decimal places as needed.
2. **\( P(z \leq 1) \)**
- Probability calculation: \( 0.841 \)
- Notes: Round to three decimal places as needed.
3. **\( P(z < 1) \)**
- Probability calculation: \( 0.841 \)
- Notes: Round to three decimal places as needed.
4. **\( P(z > 1) \)**
- Probability calculation: [Requires calculation]
5. **\( P(-1 \leq z \leq 1) \)**
- Notes: Represents the probability that \( z \) falls within 1 standard deviation from the mean.
6. **\( P(-2 \leq z \leq 2) \)**
- Notes: Represents the probability that \( z \) falls within 2 standard deviations from the mean.
7. **\( P(-2.94 \leq z \leq 0.31) \)**
- Notes: Calculate probability for specific range.
8. **\( P(-0.04 < z < 1.89) \)**
- Notes: Calculate probability for specific range.
**Instructions:**
- When probability values are calculated, ensure they are rounded to three decimal places for consistency.
- These probabilities are derived from the standard normal distribution which is symmetric around a mean of 0 with a standard deviation of 1.
- Make use of z-tables or statistical software to find these probabilities accurately.
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