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tiny-mole [99]
2 years ago
13

Points A, B, and C are collinear, and B lies

Mathematics
1 answer:
olya-2409 [2.1K]2 years ago
3 0

Answer:

BC = 30

Step-by-step explanation:

If the three points are collinear, it means they lie on the same straight line.

Now B lies between A and C

By mathematical convention;

AC = AB + BC

This means;

48 = 2x + 2 + 3x + 6

48 = 5x + 8

48-8 = 5x

5x = 40

x = 40/5

x = 8

From the question BC = 3x + 6

Substitute the value of x; 3(8) + 6 = 24 + 6 = 30

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Step-by-step explanation:

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A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a
zaharov [31]

Answer:

a) P(X>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)

And we can find this probability using the complement rule:

P(z>-1.25)=1-P(z

b) P(X

And we can find this probability uing the normal standard table:

P(z

c) P(3.5

And we can find this probability with this difference:

P(-1.25

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-1.25

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

X \sim N(5,1.2)  

Where \mu=5 and \sigma=1.2

We are interested on this probability

P(X>3.5)

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>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)

And we can find this probability using the complement rule:

P(z>-1.25)=1-P(z

Part b

We are interested on this probability

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}

If we apply this formula to our probability we got this:

P(X

And we can find this probability uing the normal standard table:

P(z

Part c

P(3.5

And we can find this probability with this difference:

P(-1.25

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-1.25

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