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3 years ago

Can anyone help with this please, I am so stuck!

Mathematics

1 answer:

Finger [1]3 years ago

4 0

Answer:

(x + 1)^2 + (y - 4)^2 = 8

Step-by-step explanation:

Midpoint of the diameter is the centre

So....Centre coordinates are ((-3+1)÷2 ; (2+6)÷2) = (-1;4)

Calculate the radius of the circle....

Radius = square root of [(-1+3)^2 + (4-2)^2]

;Radius = square root of 8

Then substitute the x-coordinate of the centre into the first slot....then the y-coordinate into the second slot and the radius(squared) into last slot of the equation......;

(x + 1)^2 + (y - 4)^2 = 8

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3 years ago

A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. (a) Describe the

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Answer:

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$P(Z$

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Step-by-step explanation:

For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

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

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

We want this probability:

$P(\bar X>89)$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 89 we got:

$z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

Part c

$P(\bar X$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 75.65 we got:

$z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

Part d

We want this probability:

$P(79.4 < \bar X < 89.3)$

We find the z scores:

$z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

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