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lidiya [134]
2 years ago
9

The equation of the line in the graph is y = (blank) x+ (blank)

Mathematics
1 answer:
Bezzdna [24]2 years ago
5 0

\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \: y=-x-1

____________________________________

\large \tt Solution  \: :

Taking two points : (-1 , 0) and (0 , -1)

\textsf{Calculate slope (m)}

\qquad \tt \rightarrow \: m =  \cfrac{rise}{run}

\qquad \tt \rightarrow \: m =  \cfrac{y_2 - y_1}{x_2 - x_1}

\qquad \tt \rightarrow \: m =  \cfrac{0 - ( - 1)}{ - 1 - 0}

\qquad \tt \rightarrow \:  m =  \cfrac{0 + 1}{ - 1}

\qquad \tt \rightarrow \:  m =   - 1

\textsf{Y - intercept (c) of graph = -1 }

Equation of line in slope - intercept form :

\qquad \tt \rightarrow \: y = mx + c

\qquad \tt \rightarrow \: y =  - x - 1

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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Answer:

a=502 +1.28*81=605.68

So the value of height that separates the bottom 90% of data from the top 10% is 605.68.  

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

X \sim N(502,81)  

Where \mu=502 and \sigma=81

We want to find a value a, such that we satisfy this condition:

P(X>a)=0.1   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.28

And if we solve for a we got

a=502 +1.28*81=605.68

So the value of height that separates the bottom 90% of data from the top 10% is 605.68.  

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x

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a

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2

,

b

=

1

, and

c

=

−

5

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x

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2

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−

1

±

√

1

2

−

4

⋅

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⋅

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