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
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Chapter1: Starting With Matlab
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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


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**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 \( \mu \):**
  \[
Transcribed Image Text:**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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