Question

Asked Mar 1, 2019

Step 1

**Confidence Interval:**

The form of the confidence interval is,

*CI *= Point estimate ± Margin of error

The approximate 100*(1–α)% confidence interval for the population mean will be obtained using the formula given below:

Step 2

**Obtain the critical value:**

The required confidence level is 100*(1–α)% = 99%.

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 population of lengths in words of the essays written for a contest is normally distributed and the population standard deviation is known.

From the given common *z-*values using standard normal distribution the critical value is obtained as 2.576 from the calculation given below:

Step 3

**Find the 99% confidence interval for the population mean length of words:**

Given that, the population standard deviation is σ = 442,

The sample mean is *x*-bar = 1,330,

The sample size is *n *= 24,

The critical value is *z*(α/2) = *z*0.005 = ...

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