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the standard deviation for the number of people with the gene ble, round to 1 decimal place.)

the standard deviation for the number of people with the gene ble, round to 1 decimal place.)

MATLAB: An Introduction with Applications
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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### Calculating the Standard Deviation for Genetic Mutation in a Population Sample **Problem Statement:** About 2% of the population has a particular genetic mutation. 500 people are randomly selected. **Objective:** Find the standard deviation for the number of people with the genetic mutation in such groups of 500. (If possible, round to 1 decimal place.) **Solution:** To determine the standard deviation in this context, we can use the formula for the standard deviation of a binomial distribution: \[ \sigma = \sqrt{n \times p \times (1 - p)} \] where: - \( n \) is the sample size (500 in this case), - \( p \) is the probability of an individual having the mutation (0.02 in this case). Substitute the given values into the formula: \[ \sigma = \sqrt{500 \times 0.02 \times (1 - 0.02)} \] \[ \sigma = \sqrt{500 \times 0.02 \times 0.98} \] \[ \sigma = \sqrt{500 \times 0.0196} \] \[ \sigma = \sqrt{9.8} \] \[ \sigma \approx 3.1 \] Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately **3.1**.
Transcribed Image Text:### Calculating the Standard Deviation for Genetic Mutation in a Population Sample **Problem Statement:** About 2% of the population has a particular genetic mutation. 500 people are randomly selected. **Objective:** Find the standard deviation for the number of people with the genetic mutation in such groups of 500. (If possible, round to 1 decimal place.) **Solution:** To determine the standard deviation in this context, we can use the formula for the standard deviation of a binomial distribution: \[ \sigma = \sqrt{n \times p \times (1 - p)} \] where: - \( n \) is the sample size (500 in this case), - \( p \) is the probability of an individual having the mutation (0.02 in this case). Substitute the given values into the formula: \[ \sigma = \sqrt{500 \times 0.02 \times (1 - 0.02)} \] \[ \sigma = \sqrt{500 \times 0.02 \times 0.98} \] \[ \sigma = \sqrt{500 \times 0.0196} \] \[ \sigma = \sqrt{9.8} \] \[ \sigma \approx 3.1 \] Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately **3.1**.
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