MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Finding the Mean and Standard Deviation of Binomial Random Variables**

To calculate the mean and standard deviation for each binomial random variable, follow these instructions. Ensure you round the mean to two decimal places and the standard deviation to four decimal places as needed.

### Given Problems:

**a.** \( n = 56 \), \( \pi = 0.95 \)

- **Mean:** 53.20
- **Standard Deviation:** *(Input required)*

**b.** \( n = 95 \), \( \pi = 0.75 \)

- **Mean:** 71.25
- **Standard Deviation:** *(Input required)*

**c.** \( n = 48 \), \( \pi = 0.90 \)

- **Mean:** 43.20
- **Standard Deviation:** *(Input required)*

### Instructions:
1. **Calculating the Mean:**
   - Formula: \( \text{Mean} = n \times \pi \)
   - Substitute the values for \( n \) and \( \pi \) from each problem.

2. **Calculating the Standard Deviation:**
   - Formula: \( \text{Standard Deviation} = \sqrt{n \times \pi \times (1 - \pi)} \)
   - Substitute the values for \( n \) and \( \pi \) from each problem.
  
Ensure all calculations are rounded correctly as specified.
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Transcribed Image Text:**Finding the Mean and Standard Deviation of Binomial Random Variables** To calculate the mean and standard deviation for each binomial random variable, follow these instructions. Ensure you round the mean to two decimal places and the standard deviation to four decimal places as needed. ### Given Problems: **a.** \( n = 56 \), \( \pi = 0.95 \) - **Mean:** 53.20 - **Standard Deviation:** *(Input required)* **b.** \( n = 95 \), \( \pi = 0.75 \) - **Mean:** 71.25 - **Standard Deviation:** *(Input required)* **c.** \( n = 48 \), \( \pi = 0.90 \) - **Mean:** 43.20 - **Standard Deviation:** *(Input required)* ### Instructions: 1. **Calculating the Mean:** - Formula: \( \text{Mean} = n \times \pi \) - Substitute the values for \( n \) and \( \pi \) from each problem. 2. **Calculating the Standard Deviation:** - Formula: \( \text{Standard Deviation} = \sqrt{n \times \pi \times (1 - \pi)} \) - Substitute the values for \( n \) and \( \pi \) from each problem. Ensure all calculations are rounded correctly as specified.
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