Mathematics: The length, in words, of the essays written for a contest are normally distributed with a population standard deviation of 565 words and an unknown population mean. If a random sample of 17 essays is taken and results in a sample mean of 940 words, find the error bound (EBM) of the confidence interval with a 90% confidence level.

First, find the decimal of 3/4 so that 0,75 multiplied by 500 is 375 seats are filled....

The length, in words, of the essays written for

gatita70

21.01.2022

The error bound (EBM) of the confidence interval with a 90% confidence level is 217.44 words.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of 1-0.05 = 0.95 , so z = 1.645

Now, find the error bound M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.645*\frac{565}{\sqrt{17}} = 217.44$

The error bound (EBM) of the confidence interval with a 90% confidence level is 217.44 words.

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