2 – (–8) (–3) = a. 14 b. 1 c. 12 d. 7

Find the center and radius of the circle

abruzzese [7]

How do we answer is there’s no pic??

8 0

2 years ago

In 2002, the mean age of an inmate on death row was 40.7 years with a standard deviation of 9.6 years according to the U.S. Depa

marissa [1.9K]

Answer:

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

Step-by-step explanation:

The confidence interval 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 level of significance $\\ \alpha$ is 1 - 0.95 = 0.05. In this case, then, we have that the z-score 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 standard normal table, 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 normal distribution. 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:

Upper limit:

$\\ 38.9 + 3.326229$

$\\ 42.226229 \approx 42.23$ years.

Lower limit:

$\\ 38.9 - 3.326229$

$\\ 35.573771 \approx 35.57$ 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.

Notice that the "mean age of an inmate on death row was 40.7 years in 2002", and this value is between the limits of the 95% confidence interval obtained. So, according to the random sample under study, it seems that this mean age has not changed.

7 0

3 years ago

The conditional relative frequency table was generated using data that compares the number of voters in the last election and wh

lidiya [134]

Using proportions, it is found that 66 people in the survey worked on election day.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For this problem, the amounts of people who worked are:

64% of 50(voted).

40% of 85(did not vote).

Hence the total amount is given by:

0.64 x 50 + 0.4 x 85 = 66.

66 people in the survey worked on election day.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

6 0

1 year ago

Decrease 216 by 37 1/2%

Anon25 [30]

Step-by-step explanation:

In this question we need to decrease 216 by $37\dfrac{1}{2}\%$ or 37.5 %.

For this, firstly find 37.5 % of 216.

$37.5\%\ \text{of}\ 216=\dfrac{37.5}{100}\times 216\\\\=81$

Now subtracting 81 from 216 to find decrease of 216 by 37.5 %.

So,

216-81 = 135

Hence, 135 is the decrease of 216 by 37.5 %.

8 0

3 years ago

Jean bought a bag of candy that contained red candies, green candies, and brown candies. Some candies are marked with a smile an

lana66690 [7]

| Red |Green | Brown Total
Smile |0.100 | .300 | .10 0.50
No smile |0.200 | .150 | .15 0.50
Total 0.30 0.45 0.25 1.00

The probability of choosing red candy is 0.10
The probability of choosing no smile candy is 0.50

The probability of choosing red or no smile = 0.10 + 0.50 = 0.60

I did not use 0.30 as the probability of red because it included the no smile candy. It should only be red candy that has a smile.

6 0

3 years ago

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