### Understanding Binomial Distribution#### Problem StatementAbout 40% of a population are of a particular ethnic group. 110 people are randomly selected from this population. Round all answers to 3 decimal places.#### Steps to Solve1. **Convert the percentage of the population to a decimal:** \( p: \) [Input Box]2. **Compute the mean and standard deviation of this size sample of this binomial distribution:** **Mean:** \(\mu: \) [Input Box] **Standard Deviation:** \(\sigma: \) [Input Box]### Explanation1. **Convert Percentage to Decimal:** To convert a percentage to a decimal, divide the percentage by 100. Formula: \( \text{Decimal Value} = \frac{\text{Percentage}}{100} \)2. **Computing the Mean of a Binomial Distribution:** The mean (\(\mu\)) of a binomial distribution is calculated using the formula: \[ \mu = n \times p \] where \( n \) is the number of trials and \( p \) is the probability of success.3. **Computing the Standard Deviation of a Binomial Distribution:** The standard deviation (\(\sigma\)) of a binomial distribution is calculated using the formula: \[ \sigma = \sqrt{n \times p \times (1 - p)} \] This measures the dispersion of the sample proportions.### ApplicationGiven:- \( n = 110 \)- \( p = 0.40 \) (from the first input box after converting 40% to a decimal)#### Example Calculation1. **Decimal Conversion:** If initially given 40%, converting this to a decimal: \[ p = \frac{40}{100} = 0.400 \]2. **Mean Calculation:** \[ \mu = 110 \times 0.40 = 44.000 \]3. **Standard Deviation Calculation:** \[ \sigma = \sqrt{110 \times 0.40 \times (1 - 0.40)} \] \[ \sigma = \sqrt{110 \times 0.40 \times 0.60} \

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About 40% of a population are of a particular ethnic group. 110 people are randomly selected from this population. Round all answers to 3 decimal places. Convert the percentage of the population to a decimal: p: Compute the mean and standard of this size sample of this binomial distribution: Mean: Standard Deviation:

About 40% of a population are of a particular ethnic group. 110 people are randomly selected from this population. Round all answers to 3 decimal places. Convert the percentage of the population to a decimal: p: Compute the mean and standard of this size sample of this binomial distribution: Mean: 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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