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iren2701 [21]
3 years ago
15

The equation of a circle C, with centre O, is:

Mathematics
1 answer:
Nataliya [291]3 years ago
8 0

Answer:

a) The center coordinates O is  (0,0)

b) The radius C = 15

Step-by-step explanation:

The given equation of the circle is : x^{2}  +  y^{2}  = 225

Now, general form of the equation of the circle is:

(x-h)^{2}  + (y - k)^{2}   = r^{2}

where (h,k) are the center co -ordinates and r is the radius of the circle.

Comparing the general equation with the given equation, we get

(x-0)^{2}  + (y - 0)^{2}   = (15)^{2}

So, here the center coordinates (h,k) = (0,0)

And the radius of the given circle is r = 15

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Answer:

a) The 99% confidence interval would be given (0.523;0.577).

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Step-by-step explanation:

Data given and notation  

n=2341 represent the random sample taken    

X represent the people that they have watched digitally streamed TV programming on some type of device

\hat p=0.55 estimated proportion of people that they have watched digitally streamed TV programming on some type of device  

\alpha=0.01 represent the significance level

Confidence =0.99 or 99%

z would represent the statistic for the confidence interval  

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p \sim N (p, \sqrt{\frac{p(1-p)}{n}}

Part a) Confidence interval

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 99% confidence interval the value of \alpha=1-0.99=0.01 and \alpha/2=0.005, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.58

And replacing into the confidence interval formula we got:

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And the 99% confidence interval would be given (0.523;0.577).

We are 99% confident that this interval contains the true population proportion.

Part b) What sample size would be required for the width of a 99% CI to be at most 0.03 irrespective of the value of p??

The margin of error for the proportion interval is given by this formula:  

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And on this case we have that ME =\pm 0.03 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.55(1-0.55)}{(\frac{0.03}{2.58})^2}=1830.51  

And rounded up we have that n=1831

8 0
4 years ago
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