**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.

Mean and standard deviation for binomial distribution

Find the mean and standard deviation for each binomial random variable: a. n = 56, T = .95 (Round your mean value to 2 decimal places and standard deviation to 4 decimal places.) Mean 53.20 Standard deviation

Find the mean and standard deviation for each binomial random variable: a. n = 56, T = .95 (Round your mean value to 2 decimal places and standard deviation to 4 decimal places.) Mean 53.20 Standard deviation

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

**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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