The answer is A. Always.
The diameter of a circle is a line that goes from one side to the other hence passing through the center!
Hope this helped!
Answer:
umm I think it 186
Step-by-step explanation:
Answer:
9 miles
Step-by-step explanation:
3 x 3 = 9 miles per day
Answer:
He must lose 4.4 pounds per week.
Step-by-step explanation:
Buffalo Bill currently weighs 202 lb. He wants to weigh 180 lbs for his reunion.
This means that he needs to lose 202 - 180 = 22 lb.
35 days from today.
Each week has 7 days. So this is 35/7 = 5 weeks from now.
How many pounds per week must he lose?
22 pounds in 5 weeks, that is 22/5 = 4.4 pounds per week.
Answer:
a) ![\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})](https://tex.z-dn.net/?f=%20%5Cbar%20X%20%5Csim%20N%20%28%5Cmu%2C%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%29)
With:
![\mu_{\bar X}= 83](https://tex.z-dn.net/?f=%5Cmu_%7B%5Cbar%20X%7D%3D%2083)
![\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3](https://tex.z-dn.net/?f=%5Csigma_%7B%5Cbar%20X%7D%3D%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%3D%203)
b) ![z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B89-83%7D%7B%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%7D%3D%202)
![P(Z>2) = 1-P(Z](https://tex.z-dn.net/?f=%20P%28Z%3E2%29%20%3D%201-P%28Z%3C2%29%3D%201-0.97725%3D%200.02275)
c) ![z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B75.65-83%7D%7B%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%7D%3D%20-2.45)
![P(Z](https://tex.z-dn.net/?f=%20P%28Z%3C-2.45%29%20%3D0.0071)
d) ![z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B89.3-83%7D%7B%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%7D%3D%202.1)
![z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B79.4-83%7D%7B%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%7D%3D%20-1.2)
![P(-1.2](https://tex.z-dn.net/?f=%20P%28-1.2%3CZ%3C2.1%29%3D%20P%28Z%3C2.1%29%20-P%28z%3C-1.2%29%20%3D%200.982-0.115%3D%200.867)
Step-by-step explanation:
For this case we know the following propoertis for the random variable X
![\mu = 83, \sigma = 27](https://tex.z-dn.net/?f=%5Cmu%20%3D%2083%2C%20%5Csigma%20%3D%2027)
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}})](https://tex.z-dn.net/?f=%20%5Cbar%20X%20%5Csim%20N%20%28%5Cmu%2C%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%29)
With:
![\mu_{\bar X}= 83](https://tex.z-dn.net/?f=%5Cmu_%7B%5Cbar%20X%7D%3D%2083)
![\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3](https://tex.z-dn.net/?f=%5Csigma_%7B%5Cbar%20X%7D%3D%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%3D%203)
Part b
We want this probability:
![P(\bar X>89)](https://tex.z-dn.net/?f=P%28%5Cbar%20X%3E89%29)
We can use the z score formula given by:
![z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
And if we find the z score for 89 we got:
![z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B89-83%7D%7B%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%7D%3D%202)
![P(Z>2) = 1-P(Z](https://tex.z-dn.net/?f=%20P%28Z%3E2%29%20%3D%201-P%28Z%3C2%29%3D%201-0.97725%3D%200.02275)
Part c
![P(\bar X](https://tex.z-dn.net/?f=P%28%5Cbar%20X%3C75.65%29)
We can use the z score formula given by:
![z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
And if we find the z score for 75.65 we got:
![z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B75.65-83%7D%7B%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%7D%3D%20-2.45)
![P(Z](https://tex.z-dn.net/?f=%20P%28Z%3C-2.45%29%20%3D0.0071)
Part d
We want this probability:
![P(79.4 < \bar X < 89.3)](https://tex.z-dn.net/?f=%20P%2879.4%20%3C%20%5Cbar%20X%20%3C%2089.3%29)
We find the z scores:
![z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B89.3-83%7D%7B%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%7D%3D%202.1)
![z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B79.4-83%7D%7B%5Cfrac%7B27%7D%7B%5Csqrt%7B81%7D%7D%7D%3D%20-1.2)
![P(-1.2](https://tex.z-dn.net/?f=%20P%28-1.2%3CZ%3C2.1%29%3D%20P%28Z%3C2.1%29%20-P%28z%3C-1.2%29%20%3D%200.982-0.115%3D%200.867)