What's the curved line with the two parallel lines

The sample mean is a statistic. True or false

ruslelena [56]

Answer:

true

Step-by-step explanation:

6 0

3 years ago

Given f(x) = x3 – 2x2 – x + 2, <br><br> the roots of f(x)

anyanavicka [17]

f(x) = x³ – 2x² – x + 2

0 = x3 – 2x2 – x + 2

(x-2)(x-1)(x+1)=0

x1=-1

x2=1

x3=2

5 0

3 years ago

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What is the area of this triangle? A=bh2 17 m² 30 m² 60 m² 120 m² Right triangle with height labeled 12 m, base labeled 5 m, and

vichka [17]

Answer:

30 m²

Step-by-step explanation:

What is the area of this triangle? A=bh/2 17 m² 30 m² 60 m² 120 m² Right triangle with height labeled 12 m, base labeled 5 m, and third side labeled 13 m.

Area of a triangle = bh/2

b = Base = 5m

h = Height = 12m

Area of the triangle = 5m × 12m/2

= 60m²/2

= 30 m²

6 0

3 years ago

License plate numbers come in a variety of styles. (Ignore the fact that some choices of letters could not be used because they

avanturin [10]

Five digit is the answer

3 0

3 years ago

An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68\%68%68, percent confidence

Komok [63]

Answer:

B. 10000 years old, with a margin of error of 400 years

Step-by-step explanation:

Assuming this complete problem: "12. An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68% confidence level, the spectrometer estimates that the branch was 10,000 years old with a following could the spectrometer estimate as the age of the branch at the 95% confidence level?"

The possible options are:

A. 9500 years old, with a margin of error of 500 years

B. 10000 years old, with a margin of error of 400 years

C. 9500 years olds, with a margin of error of 50 years

D. 10000 years old, with a margin of error of 40 year

Solution to the problem

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error for this case is given by this formula:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

For the first case the confidence was 68% so then $\alpha =1-0.68 =0.32$ and $\alpha/2 =0.16$ we can find a critical value on the normal standard distribution that accumulates 0.16 of the area on each tail and this value is $z=\pm 0.994$ , because P(z<-0.944) = 0.16 and P(Z>.944) = 0.16

The margin of error can be expressed like this:

$ME = z_{\alpha/2} SE$

We can solve for the standard error on this case and we got:

$SE = \frac{ME}{z_{\alpha/2}} =\frac{200}{0.994}=201.207$

And then for the new confidence interval we need to calculate the new $z_{\alpha}$ . For the first case the confidence was 95% so then $\alpha =1-0.95 =0.05$ and $\alpha/2 =0.025$ we can find a critical value on the normal standard distribution that accumulates 0.025 of the area on each tail and this value is $z=\pm 1.96$ , because P(z<-1.96) = 0.025 and P(Z>1.96) = 0.025. So then the new margin of error would be:

$ME = z_{\alpha/2} SE = 1.96*201.207=394.366$

The estimation for the mean not changes and from the before and new case is 1000 years. So then the best option for this case would be:

B. 10000 years old, with a margin of error of 400 years

And makes sense since a larger confidence interval means a wider interval.

8 0

3 years ago