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Mariulka [41]
3 years ago
5

Is the relationship shown by the data linear? If so, model the data with an equation. X:1,5,9,13 Y:5,10,15,20

Mathematics
1 answer:
ryzh [129]3 years ago
3 0
Let
A (x1,y1)-------> (1,5)
B (x2,y2)------> (5,10)
C (x3,y3)------> (9,15)
D (x4,y4)------> (13,20)

find the slope
AB
m=(10-5)/(5-1)-----> m=5/4

find the slope
CB
m=(15-10)/(9-5)-----> m=5/4

find the slope 
DC
m=(20-15)/(13-9)-----> m=5/4

so
<span>the relationship shown is linear
</span>
<span>to model the data with an equation find the equation of a line
</span>with m=5/4 and point A (1,5)
y-y1=m*(x-x1)-----> y-5=(5/4)*(x-1)----> y=1.25x-1.25+5-----> y=1.25x+3.75

the equation to model data is
y=1.25x+3.75

see the attached  figure

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The number of cars running a red light in a day, at a given intersection, possesses a distribution with a mean of 3.6 cars and a
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Answer:

X \sim N(3.6,5)  

Where \mu=3.6 and \sigma=5

Then we have:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

With the following parameters:

\mu_{\bar X}= 3.6

\sigma_{\bar X} = \frac{5}{\sqrt{100}}= 0.5

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 cars running a red light of a population, and for this case we know the distribution for X is given by:

X \sim N(3.6,5)  

Where \mu=3.6 and \sigma=5

Since the distribution for X is normal then we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

With the following parameters:

\mu_{\bar X}= 3.6

\sigma_{\bar X} = \frac{5}{\sqrt{100}}= 0.5

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3 years ago
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