The North Star is approximately 4,085 trillion kilometers away from earth. If 1 light

Mathematics

1 answer:

kumpel [21]2 years ago

6 0

Answer:

I don't get the question meaning

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son4ous [18]

There is a relationship between confidence interval and standard deviation:
$\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}$
Where $\overline{x}$ is the mean, $\sigma$ is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first:
$\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}$
When we do all the calculations we find that:
$\overline{x}=123.8\\ \sigma=11.84$
Now we can find confidence intervals:
$($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\$
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing

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