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2 years ago

8

PLEASE HELP FOR 100 POINTS AND BRAINLIEST! Find the unknown measures. Round lengths to the nearest hundredth and angle measures

to the nearest degree.
BC ≈ 2.52; AB ≈ 1.28; m∠C = 27°

BC ≈ 1.28; AB ≈ 2.52; m∠C = 117°

BC ≈ 1.28; AB ≈ 2.52; m∠C = 27°

BC ≈ 2.52; AB ≈ 1.28; m∠C = 117°

1 answer:

Varvara68 [4.7K]2 years ago

3 0

Answer:

A. BC ≈ 2.52; AB ≈ 1.28; m∠C = 27°

B. BC ≈ 1.28; AB ≈ 2.52; m∠C = 27°

C. BC ≈ 2.52; AB ≈ 1.28; m∠C = 117°

D. BC ≈ 1.28; AB ≈ 2.52; m∠C = 117°

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The <em>95% confidence interval</em> for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

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The <em>confidence interval</em> of the mean is given by the next formula:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$ [1]

We already know (according to the U.S. Department of Justice):

The (population) standard deviation for this case (mean age of an inmate on death row) has a standard deviation of 9.6 years ( $\\ \sigma = 9.6$ years).
The number of observations for the sample taken is $\\ n = 32$ .
The sample mean, $\\ \overline{x} = 38.9$ years.

For $\\ z_{1-\frac{\alpha}{2}}$ , we have that $\\ \alpha = 0.05$ . That is, the <em>level of significance</em> $\\ \alpha$ is 1 - 0.95 = 0.05. In this case, then, we have that the <em>z-score</em> corresponding to this case is:

$\\ z_{1-\frac{\alpha}{2}} = z_{1-\frac{0.05}{2}} = z_{1-0.025} = z_{0.975}$

Consulting a cumulative <em>standard normal table</em>, available on the Internet or in Statistics books, to find the z-score associated to the probability of, $\\ P(z$ , we have that $\\ z = 1.96$ .

Notice that we supposed that the sample is from a population that follows a <em>normal distribution</em>. However, we also have a value for n > 30, and we already know that for this result the sampling distribution for the sample means follows, approximately, a normal distribution with mean, $\\ \mu$ , and standard deviation, $\\ \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$ .

Having all this information, we can proceed to answer the question.

Constructing the 95% confidence interval for the current mean age of death-row inmates

To construct the 95% confidence interval, we already know that this interval is given by [1]:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

That is, we have:

$\\ \overline{x} = 38.9$ years.

$\\ z_{1-\frac{\alpha}{2}} = 1.96$

$\\ \sigma = 9.6$ years.

$\\ n = 32$

Then

$\\ 38.9 \pm 1.96*\frac{9.6}{\sqrt{32}}$

$\\ 38.9 \pm 1.96*\frac{9.6}{5.656854}$

$\\ 38.9 \pm 1.96*1.697056$

$\\ 38.9 \pm 3.326229$

Therefore, the Upper and Lower limits of the interval are:

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$\\ 42.226229 \approx 42.23$ years.

Lower limit:

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$\\ 35.573771 \approx 35.57$ years.

In sum, the 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

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