10. The ages of the population of a town are normally distributed with mean 43 and standard deviation 14. The town has a population of 5,000. How many would you expect to be aged between 22 and 57? Use the following Standard Normal Distribution curve: 19.1% 19.1% 15.0% 15.0% 9.2% 9.2% 0.1% 0.5% 4.4% 1.7% 0.5% 0.1% 4.4% 1.7% -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3
10. The ages of the population of a town are normally distributed with mean 43 and standard deviation 14. The town has a population of 5,000. How many would you expect to be aged between 22 and 57? Use the following Standard Normal Distribution curve: 19.1% 19.1% 15.0% 15.0% 9.2% 9.2% 0.1% 0.5% 4.4% 1.7% 0.5% 0.1% 4.4% 1.7% -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3
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
![**Problem Statement:**
The ages of the population of a town are normally distributed with a mean of 43 and a standard deviation of 14. The town has a population of 5,000. How many would you expect to be aged between 22 and 57?
**Solution Approach:**
To solve this, use the provided Standard Normal Distribution curve.
**Graph Explanation:**
The graph is a bell-shaped curve, typical of a standard normal distribution, with the mean at the center (0) and standard deviations marked along the x-axis from -3 to 3. The percentages in the graph represent the proportion of the population within each segment:
- From -3 to -2.5: 0.1%
- From -2.5 to -2: 0.5%
- From -2 to -1.5: 1.7%
- From -1.5 to -1: 4.4%
- From -1 to -0.5: 9.2%
- From -0.5 to 0: 15.0%
- From 0 to 0.5: 19.1%
- From 0.5 to 1: 19.1%
- From 1 to 1.5: 15.0%
- From 1.5 to 2: 9.2%
- From 2 to 2.5: 4.4%
- From 2.5 to 3: 1.7%
- Beyond 3: 0.1%
**Calculation Steps:**
1. Convert ages 22 and 57 to z-scores:
\[
z = \frac{(X - \text{mean})}{\text{standard deviation}}
\]
For 22:
\[
z = \frac{(22 - 43)}{14} = -1.5
\]
For 57:
\[
z = \frac{(57 - 43)}{14} = 1
\]
2. Use these z-scores to identify the area under the curve.
- From z = -1.5 to z = 1:
- -1.5 to 0: 9.2% + 15.0% = 24.2%
- 0 to 1: 19.1%](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb3b9bba-00e1-4d71-97c7-f81f90965c27%2F23194df1-4920-44bc-918c-b6f4f1362bdd%2Fk0u7w8p_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The ages of the population of a town are normally distributed with a mean of 43 and a standard deviation of 14. The town has a population of 5,000. How many would you expect to be aged between 22 and 57?
**Solution Approach:**
To solve this, use the provided Standard Normal Distribution curve.
**Graph Explanation:**
The graph is a bell-shaped curve, typical of a standard normal distribution, with the mean at the center (0) and standard deviations marked along the x-axis from -3 to 3. The percentages in the graph represent the proportion of the population within each segment:
- From -3 to -2.5: 0.1%
- From -2.5 to -2: 0.5%
- From -2 to -1.5: 1.7%
- From -1.5 to -1: 4.4%
- From -1 to -0.5: 9.2%
- From -0.5 to 0: 15.0%
- From 0 to 0.5: 19.1%
- From 0.5 to 1: 19.1%
- From 1 to 1.5: 15.0%
- From 1.5 to 2: 9.2%
- From 2 to 2.5: 4.4%
- From 2.5 to 3: 1.7%
- Beyond 3: 0.1%
**Calculation Steps:**
1. Convert ages 22 and 57 to z-scores:
\[
z = \frac{(X - \text{mean})}{\text{standard deviation}}
\]
For 22:
\[
z = \frac{(22 - 43)}{14} = -1.5
\]
For 57:
\[
z = \frac{(57 - 43)}{14} = 1
\]
2. Use these z-scores to identify the area under the curve.
- From z = -1.5 to z = 1:
- -1.5 to 0: 9.2% + 15.0% = 24.2%
- 0 to 1: 19.1%
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