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vovikov84 [41]
2 years ago
10

Problem 1:

Mathematics
2 answers:
wariber [46]2 years ago
6 0

Answer:

x=1/6

Step-by-step explanation:

3x+4=9x+3

isolate x

1=6x

1/6=x

levacccp [35]2 years ago
4 0
<h3>Hello!</h3>

======================================

First, let's move all the x's to the left:

3x+4=9x+3

3x-9x+4=3

Now, move 4 to the right:

3x-9x=3-4

Combine Like Terms:

-6x=-1

Divide both sides by -6:

x=\displaystyle\frac{1}{6}

=========================================

<h3>Notes:</h3>
  • Hope everything is clear.
  • Let me know if you have any questions!
  • Always remember: \boxed{Knowledge~is~power!}
  • Good luck & enjoy your day!
<h3>Answered by:</h3>

\mathcal{Diamond} (\boxed{An~Emotional~Helper})

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Grading managers. Some companies "grade on a bell curve" to compare the performance of their managers and professional workers.
Monica [59]

Answer:

\mu = 250, \sigma = 175.781

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

X \sim N(\mu,\sigma)  

For this case we have two conditions given:

P(X

P(X>475) = 0.1 or equivalently P(X

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}

So we can find a value from the normal standard distribution that accumulates 0.1 and 0.9 of the area in the left, for this case the two values are:

z= -1.28, z=-1.28

We can verify that P(Z<-1.28) =0.1[/tex] and P(Z<1.28) =0.9[/tex]

And then using the z score we have the following formulas:

-1.28 = \frac{25 -\mu}{\sigma}   (1)

1.28 = \frac{475 -\mu}{\sigma}   (2)

If we add equations (1) and (2) we got:

\frac{25 -\mu}{\sigma} + \frac{475 -\mu}{\sigma} =0

We can multiply both sides of the equation by \sigma and we got:

25+ 475 -2 \mu = 0

\mu = \frac{500}{2}= 250

And then we can find the standard deviation for example from equation (1) and we got:

\sigma = \frac{25-250}{-1.28}=175.781

So then the answer would be:

\mu = 250, \sigma = 175.781

 

3 0
3 years ago
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