Below is a graph with a mean of -3 and a standard deviation of 3. The shaded region represents the probability of obtaining a value from this distribution that is between 0 and 1.5 ### Understanding Normal Distribution and ProbabilityBelow 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 $)**: 3- **Shaded Region**: The area under the curve between the values 0 and 1.5 on the x-axis.![Graph 1](description-of-graph)- The x-axis ranges from -9 to 3.- The y-axis indicates the probability density function values, ranging from 0 to 0.4.- The normal distribution curve peaks at -3 and symmetrically tails off towards both ends.- The shaded region is between the x-values 0 and 1.5, representing the probability of obtaining a value within this range from the given normal distribution.#### Graph 2: Corresponding Region in Standard Normal DistributionShade the corresponding region under the standard normal density curve below.#### Graph 2: Standard Normal Distribution - **Mean ($ \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.![Graph 2](description-of-graph)- The z-axis ranges from -7 to 7.- The y-axis represents the probability density function values, ranging from 0 to

The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

Answered: Below is a graph of a normal…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

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Below is a graph with a mean of -3 and a standard deviation of 3. The shaded region represents the probability of obtaining a value from this distribution that is between 0 and 1.5

### 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.

![Graph 1](description-of-graph)
- 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.

![Graph 2](description-of-graph)
- The z-axis ranges from -7 to 7.
- The y-axis represents the probability density function values, ranging from 0 to

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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