Question

Asked Feb 27, 2019

Step 1

*Margin of error:*

Margin of error is a range of values that lie above and below the sample statistic of the confidence interval; it gives the percentage of number of points that differ in the obtained results from the population value.

Margin of error is calculated as the product of critical value and standard deviation or the product of critical value and standard error of the statistic.

The general formula for obtaining margin of error is,

Step 2

**Obtain the critical value:**

The required confidence level is 100*(1–α)% = 97%.

The required conditions for using standard normal distribution to estimate the confidence interval about mean is given below:

- The population standard deviation σ must be known.
- Either the sample size (
*n*) must be greater than 30 or the population must be normally distributed.

Here, it is given that the sample size is 100 (which is greater than 30) and the population standard deviation is known.

From the given common *z-*values using standard normal distribution the critical value is obtained as 2.17 from the calculation given below:

Step 3

**Find the margin of error of the confidence interval with 97% confidence level:**

Given that, the population standard deviation is σ = 18.53,

The sample mean is *x*-bar = 112.59,

The sample size is *n *= 100,

The critical value is *z*(α/2) = *z...*

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