### Normal Distribution and ProbabilityA normal distribution has a mean of 32 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval.#### Graphs Explanation:1. **First Graph:** - **Horizontal Axis (x):** The x-axis represents the values of the random variable x, ranging from 8 to 56. - **Shaded Area (Blue):** The portion of the graph shaded in blue represents the interval from 26 to 38. This means we are looking for the probability that x is between 26 and 38. - **Distribution Curve:** The curve is a normal distribution centered at the mean value of 32, with a standard deviation of 6. ![First Graph Diagram](first_graph.png) **Probability Calculation:** - Insert the calculated probability percentage in the box provided.2. **Second Graph:** - **Horizontal Axis (x):** Similar to the first graph, the x-axis ranges from 8 to 56. - **Shaded Area (Blue):** The shaded region represents the interval from 20 to 32. Here, we seek the probability that x is between 20 and 32. - **Distribution Curve:** Again, it's a normal distribution with mean 32 and a standard deviation of 6. ![Second Graph Diagram](second_graph.png) **Probability Calculation:** - Insert the calculated probability percentage in the box provided.---### SummaryThese graphs provide visualizations for finding the probability that a randomly selected x-value falls within specified intervals of a normal distribution. You can compute these probabilities using statistical tools or z-tables for normal distributions.

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A normal distribution has a mean of 32 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval 8 14 20 26 32 38 44 50 56 8 14 20 26 32 38 44 50 56

A normal distribution has a mean of 32 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval 8 14 20 26 32 38 44 50 56 8 14 20 26 32 38 44 50 56

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

### Normal Distribution and Probability

A normal distribution has a mean of 32 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval.

#### Graphs Explanation:

1. **First Graph:**
- **Horizontal Axis (x):** The x-axis represents the values of the random variable x, ranging from 8 to 56.
- **Shaded Area (Blue):** The portion of the graph shaded in blue represents the interval from 26 to 38. This means we are looking for the probability that x is between 26 and 38.
- **Distribution Curve:** The curve is a normal distribution centered at the mean value of 32, with a standard deviation of 6.

![First Graph Diagram](first_graph.png)

**Probability Calculation:**
- Insert the calculated probability percentage in the box provided.

2. **Second Graph:**
- **Horizontal Axis (x):** Similar to the first graph, the x-axis ranges from 8 to 56.
- **Shaded Area (Blue):** The shaded region represents the interval from 20 to 32. Here, we seek the probability that x is between 20 and 32.
- **Distribution Curve:** Again, it's a normal distribution with mean 32 and a standard deviation of 6.

![Second Graph Diagram](second_graph.png)

**Probability Calculation:**
- Insert the calculated probability percentage in the box provided.

---

### Summary
These graphs provide visualizations for finding the probability that a randomly selected x-value falls within specified intervals of a normal distribution. You can compute these probabilities using statistical tools or z-tables for normal distributions.

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