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2 years ago

How do you solve this problem 5(x-3)+7=5x-8

1 answer:

4 0

5(x-3)+7=5x-8
5*x=5x 5*3=15
5x-15+7=5x-8
15+7=22
5x-22=5x-8
5x+5x=10x
10x-22=8
22+8=30
10x=30
---------- (Divide by 10 to get x alone)
10
x=3

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And we can find this probability using the complement rule and the normal standard distribution and we got:

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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 number of attacks of a population, and for this case we know the distribution for X is given by:

$X \sim N(510,14.28)$

Where $\mu=510$ and $\sigma=14.28$

We are interested on this probability

$P(X>600)$

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:

$P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)$

And we can find this probability using the complement rule and the normal standard distribution and we got:

$P(z>6.302)=1-P(z$

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