Question

Construct the indicated confidence interval for the population mean mu.

Answer 1

Using the z-distribution, the confidence interval is given by: (11.95, 12.65).

What is a z-distribution confidence interval?

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

In which:

• $\overline{x}$ is the sample mean.

• z is the critical value.

• n is the sample size.

• $\sigma$ is the standard deviation for the population.

In this problem, we have a 90% confidence level, hence$\alpha = 0.9$, z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$, so the critical value is z = 1.645.

The other parameters are given as follows:

$\overline{x} = 12.3, \sigma = 1.5, n = 50$

Hence the bounds of the interval are:

$\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 - 1.645\frac{1.5}{\sqrt{50}} = 11.95$

$\overline{x} - z\frac{\sigma}{\sqrt{n}} = 12.3 + 1.645\frac{1.5}{\sqrt{50}} = 12.65$

More can be learned about the z-distribution at brainly.com/question/25890103

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