Bridget, Brian & Caroline share some money in the ratio 4 : 9 : 4.
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The standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 is equal to 0.0121.
<h3>What is a sample proportion?</h3>A sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.
Mathematically, sample proportion can be calculated by using this formula:
Where:
- x represent the number of individuals with a specified characteristic.
- n represent the total number of individuals in a sample.
In Mathematics, the standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 can be calculated by using this formula:
Standard deviation (SD) = √(p(1 - p)/n)
Substituting the given parameters into the formula, we have;
Standard deviation (SD) = √(0.37(1 - 0.37)/1,600)
Standard deviation (SD) = √(0.37(0.63)/1,600)
Standard deviation (SD) = √(0.2331)/1,600)
Standard deviation (SD) = √0.0001457
Standard deviation (SD) = 0.0121.
Read more on standard deviation here: brainly.com/question/14467769
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The answer would look something like this:
There could also have a simplified version.
I hope this helps.
<u>Solution</u><u>:</u>
- First square both sides.
- Now, square root and square gets cancel out in the LHS. And in the RHS, apply the identity: (a + b)² = a² + 2ab + b².
- Now, transpose 4x and 4 to LHS.
- Now, do the addition and subtraction.
<u>Answer</u><u>:</u>
<u>x </u><u>=</u><u> </u><u>±</u><u> </u><u>3</u>
Hope you could understand.
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