### Probability Distribution Table#### Normal Distribution Parameters- **Mean ($ \mu $)**: 2.23- **Standard Deviation ($ \sigma $)**: 0.28#### Cumulative Probability Table| $ x_i $ | $ P(X \leq x_i) $ ||-----------|--------------------|| 1.61 | 0.0134 || 1.76 | 0.0466 || 2.39 | 0.7161 || 2.53 | 0.8580 |#### Inverse Cumulative Probability Table| $ P(X \leq x_i) $ | $ x_i $ ||---------------------|------------|| 0.10 | 1.8712 || 0.20 | 1.9943 || 0.40 | 2.1591 || 0.60 | 2.3009 || 0.80 | 2.4657 || 0.90 | 2.5888 |### Alternate Normal Distribution Parameters- **Mean ($ \mu $)**: 2.23- **Standard Deviation ($ \sigma $)**: 0.21#### Cumulative Probability Table| $ x_i $ | $ P(X \leq x_i) $ ||-----------|--------------------|| 1.61 | 0.0016 || 1.76 | 0.0126 || 2.39 | 0.7769 || 2.53 | 0.9234 |---### InstructionsClick "Save and Submit" to save and submit your answers. Click "Save All Answers" to save all answers. **Excel Output Explanation and Problem Solving**In this exercise, we are tasked with interpreting an Excel output to solve a statistical problem related to gasoline prices in Texas. The data provided represents a normal distribution scenario with specific parameters.**Excel Data Table:**1. **Column Variables:** - `x` values: Represent the gasoline price in $/gallon. - `P(X <= x)`: Represents the cumulative probability associated with each `x` value.2. **Values:** - For `x = 1.61`, `P(X <= x) = 0.0016` - For `x = 1.76`, `P(X <= x) = 0.012` - For `x = 2.39`, `P(X <= x) = 0.7769` - For `x = 2.53`, `P(X <= x) = 0.9234`**Cumulative Probability Table:**1. **Values:** - At `P(X <= x) = 0.10`, `x = 1.9609` - At `P(X <= x) = 0.20`, `x = 2.0538` - At `P(X <= x) = 0.40`, `x = 2.1768` - At `P(X <= x) = 0.60`, `x = 2.2832` - At `P(X <= x) = 0.80`, `x = 2.4067` - At `P(X <= x) = 0.90`, `x = 2.4991`**Problem Set-Up:**Given:- The average (mean) price of gasoline in Texas is $2.23.- Assume a standard normal distribution with a standard deviation of $0.28.**Question:**What value of gasoline prices ($/gallon) is greater than 90% of the gas prices in Texas?**Possible Answers:**a. $1.8712b. $1.9609c. $2.5888d. $2.4991e. None of the answers is correct**Solution:**Based on the cumulative probability data:- The prices greater than 90% of the distribution occur at the 10% cumulative level. From

Let X be the random variable of price of gallon of gasoline in Texas. E(X)=2.23 Sd(X)=0.28…

Suppose that the average price for a gallon of gasoline in Texas is $2.23. Assume that a normal distribution applies and that the standard deviation is $0.28 on this paragraph of text, use the correct excel output above to answer the following question. Ten percent of gas prices in Texas are greater than what value (in S/gallon)? Ca. 1.8712 Ob. 1.9609 Cc 2.5888 d. 2.4991 e. None of the answers is correct

Suppose that the average price for a gallon of gasoline in Texas is $2.23. Assume that a normal distribution applies and that the standard deviation is $0.28 on this paragraph of text, use the correct excel output above to answer the following question. Ten percent of gas prices in Texas are greater than what value (in S/gallon)? Ca. 1.8712 Ob. 1.9609 Cc 2.5888 d. 2.4991 e. None of the answers is correct

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

### Probability Distribution Table

#### Normal Distribution Parameters
- **Mean ($ \mu $)**: 2.23
- **Standard Deviation ($ \sigma $)**: 0.28

#### Cumulative Probability Table

| $ x_i $ | $ P(X \leq x_i) $ |
|-----------|--------------------|
| 1.61 | 0.0134 |
| 1.76 | 0.0466 |
| 2.39 | 0.7161 |
| 2.53 | 0.8580 |

#### Inverse Cumulative Probability Table

| $ P(X \leq x_i) $ | $ x_i $ |
|---------------------|------------|
| 0.10 | 1.8712 |
| 0.20 | 1.9943 |
| 0.40 | 2.1591 |
| 0.60 | 2.3009 |
| 0.80 | 2.4657 |
| 0.90 | 2.5888 |

### Alternate Normal Distribution Parameters
- **Mean ($ \mu $)**: 2.23
- **Standard Deviation ($ \sigma $)**: 0.21

#### Cumulative Probability Table

| $ x_i $ | $ P(X \leq x_i) $ |
|-----------|--------------------|
| 1.61 | 0.0016 |
| 1.76 | 0.0126 |
| 2.39 | 0.7769 |
| 2.53 | 0.9234 |

---

### Instructions
Click "Save and Submit" to save and submit your answers. Click "Save All Answers" to save all answers.

**Excel Output Explanation and Problem Solving**

In this exercise, we are tasked with interpreting an Excel output to solve a statistical problem related to gasoline prices in Texas. The data provided represents a normal distribution scenario with specific parameters.

**Excel Data Table:**

1. **Column Variables:**
- `x` values: Represent the gasoline price in $/gallon.
- `P(X <= x)`: Represents the cumulative probability associated with each `x` value.

2. **Values:**
- For `x = 1.61`, `P(X <= x) = 0.0016`
- For `x = 1.76`, `P(X <= x) = 0.012`
- For `x = 2.39`, `P(X <= x) = 0.7769`
- For `x = 2.53`, `P(X <= x) = 0.9234`

**Cumulative Probability Table:**

1. **Values:**
- At `P(X <= x) = 0.10`, `x = 1.9609`
- At `P(X <= x) = 0.20`, `x = 2.0538`
- At `P(X <= x) = 0.40`, `x = 2.1768`
- At `P(X <= x) = 0.60`, `x = 2.2832`
- At `P(X <= x) = 0.80`, `x = 2.4067`
- At `P(X <= x) = 0.90`, `x = 2.4991`

**Problem Set-Up:**

Given:
- The average (mean) price of gasoline in Texas is $2.23.
- Assume a standard normal distribution with a standard deviation of $0.28.

**Question:**
What value of gasoline prices ($/gallon) is greater than 90% of the gas prices in Texas?

**Possible Answers:**
a. $1.8712
b. $1.9609
c. $2.5888
d. $2.4991
e. None of the answers is correct

**Solution:**

Based on the cumulative probability data:
- The prices greater than 90% of the distribution occur at the 10% cumulative level. From

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