Below is a graph of a normal distribution with mean u = -3 and standard deviation O = 3. The shaded region represents the probability of obtaining a value from this distribution that is between 0 and 1.5. 0.4+ 0.3- 0.2- 0,1+ 1.5 Shade the corresponding region under the standard normal density curve below. 0.4, /0.3- ? 0.2+ 0.1- -6 -4
Below is a graph of a normal distribution with mean u = -3 and standard deviation O = 3. The shaded region represents the probability of obtaining a value from this distribution that is between 0 and 1.5. 0.4+ 0.3- 0.2- 0,1+ 1.5 Shade the corresponding region under the standard normal density curve below. 0.4, /0.3- ? 0.2+ 0.1- -6 -4
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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Below is a graph with a mean of -3 and a standard deviation of 3. The shaded region represents the
- The x-axis ranges from -9 to 3.
- The y-axis indicates the probability density function values, ranging from 0 to 0.4.
- The normal distribution curve peaks at -3 and symmetrically tails off towards both ends.
- The shaded region is between the x-values 0 and 1.5, representing the probability of obtaining a value within this range from the given normal distribution.
#### Graph 2: Corresponding Region in Standard Normal Distribution
Shade the corresponding region under the standard normal density curve below.
#### Graph 2: Standard Normal Distribution
- **Mean (\( \mu \))**: 0
- **Standard Deviation (\( \sigma \))**: 1
- To find the corresponding region, convert the x-values (0 to 1.5) to z-scores using the transformation formula: \( z = \frac{(X - \mu)}{\sigma} \).
**Transformation Process:**
1. For \( X = 0 \):
\[
z = \frac{(0 - (-3))}{3} = \frac{3}{3} = 1
\]
2. For \( X = 1.5 \):
\[
z = \frac{(1.5 - (-3))}{3} = \frac{4.5}{3} = 1.5
\]
Thus, the corresponding shaded region is the area under the standard normal distribution curve between z-scores of 1 and 1.5.
- The z-axis ranges from -7 to 7.
- The y-axis represents the probability density function values, ranging from 0 to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11ec3ece-071b-4ed7-8b14-ac1b7b533da3%2F55c30b52-44ea-4ff9-842e-933dce661757%2Fuk9ek3h_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Normal Distribution and Probability
Below is a graph of a normal distribution with a mean (\( \mu \)) of -3 and a standard deviation (\( \sigma \)) of 3. The shaded region represents the probability of obtaining a value from this distribution that is between 0 and 1.5.
#### Graph 1: Normal Distribution
- **Mean (\( \mu \))**: -3
- **Standard Deviation (\( \sigma \))**: 3
- **Shaded Region**: The area under the curve between the values 0 and 1.5 on the x-axis.
- The x-axis ranges from -9 to 3.
- The y-axis indicates the probability density function values, ranging from 0 to 0.4.
- The normal distribution curve peaks at -3 and symmetrically tails off towards both ends.
- The shaded region is between the x-values 0 and 1.5, representing the probability of obtaining a value within this range from the given normal distribution.
#### Graph 2: Corresponding Region in Standard Normal Distribution
Shade the corresponding region under the standard normal density curve below.
#### Graph 2: Standard Normal Distribution
- **Mean (\( \mu \))**: 0
- **Standard Deviation (\( \sigma \))**: 1
- To find the corresponding region, convert the x-values (0 to 1.5) to z-scores using the transformation formula: \( z = \frac{(X - \mu)}{\sigma} \).
**Transformation Process:**
1. For \( X = 0 \):
\[
z = \frac{(0 - (-3))}{3} = \frac{3}{3} = 1
\]
2. For \( X = 1.5 \):
\[
z = \frac{(1.5 - (-3))}{3} = \frac{4.5}{3} = 1.5
\]
Thus, the corresponding shaded region is the area under the standard normal distribution curve between z-scores of 1 and 1.5.
- The z-axis ranges from -7 to 7.
- The y-axis represents the probability density function values, ranging from 0 to
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