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2 years ago

I need help on this question, think any of you guys could help?

Mathematics

1 answer:

levacccp [35]2 years ago

3 0

Answer:

We need to find the circumference, and in order to find the circumference we must know the formula for it.

Formula for circumference of a circle;

a = 2πr

Where π is the pi(3.14 or 22/7), and r is the radius which is half of the diameter.

Since we are given the diameter, we need to find the radius. So 1/2 of the diameter (26 x 1/2) = is 13

Now we just plug in the actual values in the formula:

a = 2πr

a = 2 x 3.14 x 13

a = <u>18.84 feet</u>

But now, we need to find how many revolutions it would take to get to 500 feet.

So we divide 500 feet by 18.84 feet;

500/18.84 = 26.53, around 27 revolutions.

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A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec

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Answer:

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

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".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 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)

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

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$