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.

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 level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the error bound M as such

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

So

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