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goldfiish [28.3K]
3 years ago
15

Triple a number, x, increased by 1 is between -20 and 10. What are the solutions for x?

Mathematics
1 answer:
Bumek [7]3 years ago
3 0
Hello,
-20 \leq 3x+1 \leq 10\\
\Rightarrow\ -21 \leq 3x \leq 9\\
\Rightarrow\ -7 \leq x \leq 3\\

Sol=[-7\ 3]\ if\ x\ is\ a\ real.


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A researcher collected data from a sample of correctional officers and found that on average they made 47,173 dollars a year wit
ollegr [7]

Answer:

a) z = \frac{40000- 47173}{6364} = -1.127

b) z = \frac{50000- 47173}{6364} = 0.444

c) P(X>40000)=P(\frac{X-\mu}{\sigma}>\frac{40000-\mu}{\sigma})=P(Z>\frac{40000-47173}{6364})=P(z>-1.127)

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

P(z>-1.127)=1-P(z

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".  

Part a

Let X the random variable that represent the amount of money of a population of interet, and we know the following info:  

Where \bar X=47173 and s=6364

We can assume that the sample size is large and the estimators can be used as a good description for the parameters  \mu \sigma

The z score for 40000 would be:

z = \frac{40000- 47173}{6364} = -1.127

Part b

The z score for 50000 would be:

z = \frac{50000- 47173}{6364} = 0.444

Part c

We are interested on this probability

P(X>40000)

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>40000)=P(\frac{X-\mu}{\sigma}>\frac{40000-\mu}{\sigma})=P(Z>\frac{40000-47173}{6364})=P(z>-1.127)

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

P(z>-1.127)=1-P(z

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ira [324]
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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