Question

A safety auditor at a paint factory took a random sample of 25 cans of paint from a production run of over

Answer 1

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval is (29.6, 44.4).

What is a t-distribution confidence interval?

The confidence interval is:

$\overline{x} \pm t\frac{s}{\sqrt{n}}$

In which:

• $\overline{x}$ is the sample mean.

• t is the critical value.

• n is the sample size.

• s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 25 - 1 = 24 df, is t = 2.0639.

The other parameters are given by:

$\overline{x} = 37, s = 18, n = 25$.

Hence, the bounds of the interval are given as follows:

$\overline{x} - t\frac{s}{\sqrt{n}} = 37 - 2.0639\frac{18}{5} = 29.6$

$\overline{x} + t\frac{s}{\sqrt{n}} = 37 + 2.0639\frac{18}{5} = 44.4$

The 95% confidence interval is (29.6, 44.4).

More can be learned about the t-distribution at brainly.com/question/16162795

Answer 2

Answer:

To simplify what the other person said:

(29.57, 44.43)

Step-by-step explanation:

Proof that this is right on Khan