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3 years ago

Find the radius y of circle C, given that x = 12 and z = y + 8.

Mathematics

1 answer:

aivan3 [116]3 years ago

6 0

Answer:

y = 5

Step-by-step explanation:

use Pythagorean theorem

z² = x² + y²

(y + 8)² = 12² + y²

y² + 16y + 64 = 144 + y²

16y = 80

y = 5

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Answer:

$P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)$

And we can find this probability using the complement rule and with excel or the normal standard table:

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Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(10.5,0.3)$

Where $\mu=10.5$ and $\sigma=0.3$

We are interested on this probability

$P(X>10.983)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)$

And we can find this probability using the complement rule and with excel or the normal standard table:

$P(z>1.61)=1-P(z$

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