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5.7099 is the margin of error.
<h3>What is standard deviation ?</h3>
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
According to the question,
The standard sampling error of the sample mean is σₓ ,
The sampling distribution is: N (u,σₓ/n)
Therefore,
By using the standard deviation formula:
σₓ = √∑(xi -μ)/N
Where,
∑= population standard deviation
N= the size of the population
xi= each value from the population
μ =the population mean
So ,
σₓ = = 2.913
Since, a = 1- 95% = 0.05
therefore = (1-0.005 x 2) = 1.959964
Here, the margin of error for a 95% confidence interval for this sample is given by:
* σₓ = 1.959964 x 2.913
= 5.7099
5.7099 is the margin of error for a 95% confidence interval for this sample.
Learn more about standard deviation here:
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From the odd-degree terms, take out one copy and rewrite the series as
Then if |<em>x</em>| < 1, we can condense this to
Since the series we invoked here converge on -1 < <em>x</em> < 1, so does this one.