About 1% of the population has a particular genetic mutation. 100 people are randomly selected.Find the standard deviation for the number of people with the genetic mutation in such groups of 100. (Remeber that standard deviation should be rounded to one more decimal place than the raw data, in this case 1 decimal place is necessary.)

Question

03-11-2022
Mathematics

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About 1% of the population has a particular genetic mutation. 100 people are randomly selected.Find the standard deviation for the number of people with the genetic mutation in such groups of 100. (Remeber that standard deviation should be rounded to one more decimal place than the raw data, in this case 1 decimal place is necessary.)

Sagot :

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BrissaQ628569 BrissaQ628569 · Answer 1 · 2022-11-03T09:30:59-04:00

ANSWER:

1.0

STEP-BY-STEP EXPLANATION:

Given:

p = 1% = 0.01

q = 1 - p = 1 - 0.01 = 0.99

n = 100

The standard deviation is calculated using the following formula:

[tex]\begin{gathered} \sigma=\sqrt{n\cdot p\cdot q} \\ \\ \text{ We replace each value and obtain the standard deviation:} \\ \\ \sigma=\sqrt{100\cdot0.01\cdot0.99} \\ \\ \sigma=\sqrt{0.99} \\ \\ \sigma=0.99498 \\ \\ \sigma=0.995\rightarrow1\text{ decimal place}\rightarrow1.0 \end{gathered}[/tex]

Therefore, the standard deviation is equal to 1.0

Sagot :

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