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3 years ago

HELP BRAINLIEST!!!

Mathematics

1 answer:

prisoha [69]3 years ago

8 0

Answer: The correct answer is option B: The vertical angle

Step-by-step explanation: Please refer to the picture attached for further details.

The circle with center O has an arc AB with a central angle of 42 degrees as shown in the diagram (not draw to scale).

If the line A is extended to point D and also line B is extended to point C both along the circumference of the circle O, then you would have another arc CD on the circle.

If two intersecting lines AD and BC form a pair of angles (shown here as 42° and x°) the angles are called vertical angles, and vertical angles in a circle are equal.

Hence the only thing that can be shown to measure 42 degrees in the question above is a vertical angle.

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$7-1.796\frac{2.216}{\sqrt{12}}=5.851$

$7+1.796\frac{2.216}{\sqrt{12}}=8.149$

So on this case the 90% confidence interval would be given by (5.851;8.149)

Step-by-step explanation:

Previous concepts

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

Solution to the problem

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

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

Data: 7 8 2 10 6 5 7 8 8 9 5 9

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=7$

The sample deviation calculated $s=2.216$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=12-1=11$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,11)".And we see that $t_{\alpha/2}=1.796$

Now we have everything in order to replace into formula (1):

$7-1.796\frac{2.216}{\sqrt{12}}=5.851$

$7+1.796\frac{2.216}{\sqrt{12}}=8.149$

So on this case the 90% confidence interval would be given by (5.851;8.149)

3 0

3 years ago

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