EXCEL CHART:XP(X)00.90392110.09223720.00376537.68E-0547.84E-0753.2E-09Question is in the picture. **Probability Distributions and Calculations in Statistics****6. Probability Distribution and Calculator Use***Sometimes a probability distribution that is not binomial is given (chart of x and p(x)) and you’re required to determine the mean and standard deviation using the calculator.***a. What calculator keystrokes are required? Be specific.**To determine the mean and standard deviation for a given probability distribution using a calculator, follow these steps:1. **Entering Data:** - Press the `STAT` button. - Select `1: Edit` and enter your data into lists (L1 and L2). - Input the values of $ x $ into L1. - Input the corresponding probabilities $ p(x) $ into L2.2. **Calculating Mean and Standard Deviation:** - Press the `STAT` button again. - Use the arrow keys to highlight `CALC`. - Select `1: 1-Var Stats`. - Enter `L1, L2` (indicating that L1 contains $ x $ values and L2 contains $ p(x) $ values). - Press `ENTER` to calculate.The calculator will display the mean (denoted as $ \overline{x} $) and the standard deviation (denoted as $ \sigma $ or $ s $) among other statistics.**b. How does the resulting $ n $ confirm that you have not missed a step?**The resulting $ n $ represents the total number of probabilities inputted. It confirms that you haven't missed a step if the sum of the probabilities $ \sum p(x) $ equals 1 (or very close to 1, allowing for rounding errors). This is because the total probability for any distribution must sum to 1. If $ n $ does not make logical sense or the sum of probabilities does not equal 1, recheck your data entries for accuracy.**7. Sample Size and Probability in Statistics***Suppose another scenario only provides the sample size (n) and probability of success (p). Which equations are used to determine the mean and standard deviation for this situation? Be specific.*For a binomial distribution, when given the sample size $ n $ and the probability of success $ p $, the formulas to determine the mean and standard deviation are as follows:- **Mean $ \mu $:** \[

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6. Sometimes a probability distribution that is not binomial is given (chart of x and p(x)) and you're required to determine the mean and standard deviation using the calculator. a. What calculator keystrokes are required? Be specific. b. How does the resulting n confirm that you have not missed a step?

6. Sometimes a probability distribution that is not binomial is given (chart of x and p(x)) and you're required to determine the mean and standard deviation using the calculator. a. What calculator keystrokes are required? Be specific. b. How does the resulting n confirm that you have not missed a step?

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

EXCEL CHART:

X	P(X)
0	0.903921
1	0.092237
2	0.003765
3	7.68E-05
4	7.84E-07
5	3.2E-09

Question is in the picture.

**Probability Distributions and Calculations in Statistics**

**6. Probability Distribution and Calculator Use**

*Sometimes a probability distribution that is not binomial is given (chart of x and p(x)) and you’re required to determine the mean and standard deviation using the calculator.*

**a. What calculator keystrokes are required? Be specific.**

To determine the mean and standard deviation for a given probability distribution using a calculator, follow these steps:

1. **Entering Data:**
- Press the `STAT` button.
- Select `1: Edit` and enter your data into lists (L1 and L2).
- Input the values of $ x $ into L1.
- Input the corresponding probabilities $ p(x) $ into L2.

2. **Calculating Mean and Standard Deviation:**
- Press the `STAT` button again.
- Use the arrow keys to highlight `CALC`.
- Select `1: 1-Var Stats`.
- Enter `L1, L2` (indicating that L1 contains $ x $ values and L2 contains $ p(x) $ values).
- Press `ENTER` to calculate.

The calculator will display the mean (denoted as $ \overline{x} $) and the standard deviation (denoted as $ \sigma $ or $ s $) among other statistics.

**b. How does the resulting $ n $ confirm that you have not missed a step?**

The resulting $ n $ represents the total number of probabilities inputted. It confirms that you haven't missed a step if the sum of the probabilities $ \sum p(x) $ equals 1 (or very close to 1, allowing for rounding errors). This is because the total probability for any distribution must sum to 1. If $ n $ does not make logical sense or the sum of probabilities does not equal 1, recheck your data entries for accuracy.

**7. Sample Size and Probability in Statistics**

*Suppose another scenario only provides the sample size (n) and probability of success (p). Which equations are used to determine the mean and standard deviation for this situation? Be specific.*

For a binomial distribution, when given the sample size $ n $ and the probability of success $ p $, the formulas to determine the mean and standard deviation are as follows:

- **Mean $ \mu $:**
\[

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