### Calculating the Mean, Variance, and Standard Deviation of a Binomial DistributionIn this exercise, you will find the mean, variance, and standard deviation of the binomial distribution with the given values of $ n $ and $ p $.The parameters provided are:- $ n = 50 $- $ p = 0.3 $#### MeanThe mean (μ) of a binomial distribution is calculated using the formula:\[ \mu = n \cdot p \]For this example:\[ \mu = 50 \cdot 0.3 \]\[ \mu = 15 \](Note: The value should be rounded to the nearest tenth if necessary.)#### VarianceThe variance (σ²) of a binomial distribution is calculated using the formula:\[ \sigma^2 = n \cdot p \cdot (1 - p) \]Plugging in the values:\[ \sigma^2 = 50 \cdot 0.3 \cdot (1 - 0.3) \]\[ \sigma^2 = 50 \cdot 0.3 \cdot 0.7 \]\[ \sigma^2 = 10.5 \]#### Standard DeviationThe standard deviation (σ) is the square root of the variance:\[ \sigma = \sqrt{n \cdot p \cdot (1 - p)} \]Using the calculated variance:\[ \sigma = \sqrt{10.5} \]\[ \sigma \approx 3.24 \]#### Input InstructionsEnter your answer in the answer box and then click "Check Answer".### Example Screen Layout- **Remaining Parts**: 2 parts remaining shown in a progress bar.- **Action Buttons**: Clear All and Check Answer. The example screen captures a typical educational website layout where students input their calculated answers based on provided formulas. Ensure the values are rounded as specified in the instructions.---This content guides students through the statistical concepts and computational steps necessary to characterize a binomial distribution's behavior. Understanding these basics are crucial for interpreting and analyzing binomial data effectively.

Binomial distribution: The binomial distribution gives the probability of number of successes out of…

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Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n= 50, p 0.3 %3D

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

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Calculating the Mean, Variance, and Standard Deviation of a Binomial Distribution

In this exercise, you will find the mean, variance, and standard deviation of the binomial distribution with the given values of $ n $ and $ p $.

The parameters provided are:
- $ n = 50 $
- $ p = 0.3 $

#### Mean
The mean (μ) of a binomial distribution is calculated using the formula:
\[ \mu = n \cdot p \]

For this example:
\[ \mu = 50 \cdot 0.3 \]
\[ \mu = 15 \]

(Note: The value should be rounded to the nearest tenth if necessary.)

#### Variance
The variance (σ²) of a binomial distribution is calculated using the formula:
\[ \sigma^2 = n \cdot p \cdot (1 - p) \]

Plugging in the values:
\[ \sigma^2 = 50 \cdot 0.3 \cdot (1 - 0.3) \]
\[ \sigma^2 = 50 \cdot 0.3 \cdot 0.7 \]
\[ \sigma^2 = 10.5 \]

#### Standard Deviation
The standard deviation (σ) is the square root of the variance:
\[ \sigma = \sqrt{n \cdot p \cdot (1 - p)} \]

Using the calculated variance:
\[ \sigma = \sqrt{10.5} \]
\[ \sigma \approx 3.24 \]

#### Input Instructions
Enter your answer in the answer box and then click "Check Answer".

### Example Screen Layout
- **Remaining Parts**: 2 parts remaining shown in a progress bar.
- **Action Buttons**: Clear All and Check Answer.

The example screen captures a typical educational website layout where students input their calculated answers based on provided formulas. Ensure the values are rounded as specified in the instructions.

---

This content guides students through the statistical concepts and computational steps necessary to characterize a binomial distribution's behavior. Understanding these basics are crucial for interpreting and analyzing binomial data effectively.

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