a) 10th percentile b) 75th percentile c) 85th percentile Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. a) The combined scores that correspond to 10th percentile is about (Round to the nearest integer as needed.). b) The combined scores that correspond to 75th percentile is about (Round to the nearest integer as needed.). c) The combined scores that correspond to 85th percentile is about (Round to the nearest integer as needed.)
a) 10th percentile b) 75th percentile c) 85th percentile Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. a) The combined scores that correspond to 10th percentile is about (Round to the nearest integer as needed.). b) The combined scores that correspond to 75th percentile is about (Round to the nearest integer as needed.). c) The combined scores that correspond to 85th percentile is about (Round to the nearest integer 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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Question
Answer the following question by looking at the Standard normal deviation table that is provided
- [Click here to view page 2 of the standard normal distribution table.](#)
#### Questions:
a) **The combined scores that correspond to the 10th percentile is about** \[ \_\]
(Round to the nearest integer as needed.)
b) **The combined scores that correspond to the 75th percentile is about** \[ \_\]
(Round to the nearest integer as needed.)
c) **The combined scores that correspond to the 85th percentile is about** \[ \_\]
(Round to the nearest integer as needed.)
---
**Explanation of Calculation:**
To find the combined scores that correspond to specific percentiles, you'll typically use a Z-table (standard normal distribution table). Here, we convert the percentiles to Z-scores and use those Z-scores to find the corresponding test scores using the formula:
\[ X = \mu + Z \times \sigma \]
Where:
- \( X \) is the test score.
- \( \mu \) is the mean of the distribution (1493 in this case).
- \( Z \) is the Z-score.
- \( \sigma \) is the standard deviation (339 in this case).
1. **10th Percentile:**
- Find the Z-score for the 10th percentile using the Z-table.
- Substitute \( \mu \), Z-score, and \( \sigma \) into the formula to calculate the combined score.
2. **75th Percentile:**
- Find the Z-score for the 75th percentile using the Z-table.
- Substitute \( \mu \), Z-score, and \( \sigma \) into the formula to calculate the combined score.
3. **85th Percentile:**
- Find the Z-score for the 85th percentile using the Z-table.
- Substitute \( \mu \), Z-score, and \( \sigma \) into the formula to calculate the combined score.
Note: The links to the standard normal distribution table will direct](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ffd19f8-d4bd-4354-b212-3cca5c840442%2Fb7f809df-3900-4f98-9cda-6fc162faf29c%2Fxhdekz6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Combined Test Scores and Percentiles
Combined test scores were normally distributed with a mean of 1493 and a standard deviation of 339. Find the combined scores that correspond to the following percentiles:
a) 10th percentile
b) 75th percentile
c) 85th percentile
#### Useful Resources:
- [Click here to view page 1 of the standard normal distribution table.](#)
- [Click here to view page 2 of the standard normal distribution table.](#)
#### Questions:
a) **The combined scores that correspond to the 10th percentile is about** \[ \_\]
(Round to the nearest integer as needed.)
b) **The combined scores that correspond to the 75th percentile is about** \[ \_\]
(Round to the nearest integer as needed.)
c) **The combined scores that correspond to the 85th percentile is about** \[ \_\]
(Round to the nearest integer as needed.)
---
**Explanation of Calculation:**
To find the combined scores that correspond to specific percentiles, you'll typically use a Z-table (standard normal distribution table). Here, we convert the percentiles to Z-scores and use those Z-scores to find the corresponding test scores using the formula:
\[ X = \mu + Z \times \sigma \]
Where:
- \( X \) is the test score.
- \( \mu \) is the mean of the distribution (1493 in this case).
- \( Z \) is the Z-score.
- \( \sigma \) is the standard deviation (339 in this case).
1. **10th Percentile:**
- Find the Z-score for the 10th percentile using the Z-table.
- Substitute \( \mu \), Z-score, and \( \sigma \) into the formula to calculate the combined score.
2. **75th Percentile:**
- Find the Z-score for the 75th percentile using the Z-table.
- Substitute \( \mu \), Z-score, and \( \sigma \) into the formula to calculate the combined score.
3. **85th Percentile:**
- Find the Z-score for the 85th percentile using the Z-table.
- Substitute \( \mu \), Z-score, and \( \sigma \) into the formula to calculate the combined score.
Note: The links to the standard normal distribution table will direct
![# Standard Normal Distribution Table
## Understanding the Standard Normal Distribution
The standard normal distribution, often referred to as the Z-distribution, is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. The table of the standard normal distribution provides the area under the curve to the left of a given Z value (the cumulative probability). These tables are essential in statistics for calculating probabilities and critical values that correspond to Z-scores.
### How to Read the Table
The entries in the table represent the area under the curve between Z = 0 and a positive value of Z. Due to the symmetry of the standard normal distribution curve, the area under the curve for a positive Z value can also be used to find the area for a negative Z value.
### Formula Representation
The formula for the cumulative distribution function (CDF) of the standard normal distribution is:
\[ \Phi(z) = P(Z \leq z) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{z} e^{-\frac{t^2}{2}} dt \]
The table provides values for this function for various Z-scores.
### Table Representation
**Table Page 1:**
This page covers Z-scores from 0.00 to 1.09.
| Z \ 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
|----------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| 0.0 | 0.0000| 0.0040| 0.0080| 0.0120| 0.0160| 0.0199| 0.0239| 0.0279| 0.0319|
| 0.1 | 0.0398| 0.0438| 0.0478| 0.0517| 0.0557| 0.0596| 0.0636| 0.0675| 0.0714|
| 0.2 | 0.0793| 0.0832| 0.0871|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ffd19f8-d4bd-4354-b212-3cca5c840442%2Fb7f809df-3900-4f98-9cda-6fc162faf29c%2Fk7yd9hv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Standard Normal Distribution Table
## Understanding the Standard Normal Distribution
The standard normal distribution, often referred to as the Z-distribution, is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. The table of the standard normal distribution provides the area under the curve to the left of a given Z value (the cumulative probability). These tables are essential in statistics for calculating probabilities and critical values that correspond to Z-scores.
### How to Read the Table
The entries in the table represent the area under the curve between Z = 0 and a positive value of Z. Due to the symmetry of the standard normal distribution curve, the area under the curve for a positive Z value can also be used to find the area for a negative Z value.
### Formula Representation
The formula for the cumulative distribution function (CDF) of the standard normal distribution is:
\[ \Phi(z) = P(Z \leq z) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{z} e^{-\frac{t^2}{2}} dt \]
The table provides values for this function for various Z-scores.
### Table Representation
**Table Page 1:**
This page covers Z-scores from 0.00 to 1.09.
| Z \ 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
|----------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| 0.0 | 0.0000| 0.0040| 0.0080| 0.0120| 0.0160| 0.0199| 0.0239| 0.0279| 0.0319|
| 0.1 | 0.0398| 0.0438| 0.0478| 0.0517| 0.0557| 0.0596| 0.0636| 0.0675| 0.0714|
| 0.2 | 0.0793| 0.0832| 0.0871|
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