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-BARSIC- [3]
3 years ago
11

A random sample of 84 students at a university showed an average age of 22 years and a sample standard deviation of 3 years. Fin

d the margin of error for the 94% confidence interval. (Assume that the population of students is large relative to the sample size. Round your solution to 4 decimal places)
Mathematics
1 answer:
Debora [2.8K]3 years ago
7 0

Answer:

The margin of error for the 94% confidence interval is 0.6154.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population mean is:

CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

The margin of error of this interval is:

MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

The critical value of <em>z</em> for 94% confidence level is, <em>z</em> = 1.88.

Compute the margin of error for the 94% confidence interval as follows:

MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}

          =1.88\times\frac{3}{\sqrt{84}}\\\\=0.6154

Thus, the margin of error for the 94% confidence interval is 0.6154.

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Given: AC and AE are common external tangents of G and D. BC= 123 GB=20 and AG=101. What is the measure of AC?​
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Answer:

The length of AC is 222 units.

Step-by-step explanation:

Given AC and AE are common external tangents of G and D.

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We have to find the measure of AC.

As, a straight line joined from the center i.e radius is perpendicular to tangent drawn. Therefore,

In ΔABG, by Pythagoras theorem

AG^2=AB^2+BG^2

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Hence, AC=AB+BC=99+123=222 units.

The length of AC is 222 units.

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PLEASE HELP!!! :))
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For a better understanding of the solution given here please find the attached file which has the relevant diagram.

To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.

Please follow the diagram of a complete understanding of the logic and the solution.

As EF is the angle bisector as given in the question, thus we will have:

m\angle DEK=2\times m\angle DE F=2\times 43^{\circ}=86^{\circ}.

Also, from the Theorem we know that KF will be half of DK and thus, KF will be:KF=\frac{1}{2}DK= \frac{1}{2}\times 16=8 centimeters.

Likewise, from the same theorem we have: m\angle EFD=90^{\circ}

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