Find the indicated probability using the standard normal distribution. P(-2.99
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 Probability Using the Standard Normal Distribution
**Problem:**
Calculate the probability using the standard normal distribution:
\[ P(-2.99 < z < 0) \]
**Resources:**
- [View Page 1 of the Standard Normal Table](#)
- [View Page 2 of the Standard Normal Table](#)
**Instructions:**
- Determine the probability \( P(-2.99 < z < 0) \).
- Round your answer to four decimal places as needed.
**Input Box:**
\[ P(-2.99 < z < 0) = \_\_\_\_\_ \]
**Notes:**
- You have a total time of 2 hours, 47 minutes, and 55 seconds to complete this task.
- Click "Next" when ready to submit your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F275f078e-e6df-4549-aae8-3195dc20960c%2F134ab996-e633-4ffd-9ad7-2b797e05c35c%2F7yper2f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding Probability Using the Standard Normal Distribution
**Problem:**
Calculate the probability using the standard normal distribution:
\[ P(-2.99 < z < 0) \]
**Resources:**
- [View Page 1 of the Standard Normal Table](#)
- [View Page 2 of the Standard Normal Table](#)
**Instructions:**
- Determine the probability \( P(-2.99 < z < 0) \).
- Round your answer to four decimal places as needed.
**Input Box:**
\[ P(-2.99 < z < 0) = \_\_\_\_\_ \]
**Notes:**
- You have a total time of 2 hours, 47 minutes, and 55 seconds to complete this task.
- Click "Next" when ready to submit your answer.
Transcribed Image Text:**Title: Understanding the Standard Normal Distribution Table**
**Introduction:**
The table displayed provides the area under the standard normal distribution curve to the left of a given Z-value. This is a key concept in statistics, often used for determining probabilities and critical values in various statistical tests.
**Explanation of the Table:**
The table is structured with Z-values in the leftmost column, ranging from -3.4 to -2.0. The top row represents the second decimal place, ranging from 0.00 to 0.09.
**Reading the Table:**
To find the area to the left of a particular Z-score:
1. Locate the first digit and the first decimal of the Z-value in the leftmost column.
2. Identify the second decimal place across the top row.
3. The intersection of this row and column provides the cumulative probability of the Z-score.
**Example of Interpretation:**
- For a Z-score of -2.8, find -2.8 in the left column.
- Move horizontally to the column labeled .05 for the second decimal place.
- The corresponding value is .0026, indicating the probability that a value falls to the left of Z = -2.85 on the standard normal distribution curve is 0.26%.
**Application:**
This table is crucial in statistical methodologies involving normal distributions, such as hypothesis testing and confidence interval estimation. It helps in assessing how extreme or typical a given data point is within a distribution.
Understanding and utilizing this table effectively allows for accurate statistical analysis and inference in a wide range of applications, from academic research to everyday data analysis tasks.
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