One i think might be right but answer 2 is (10,0)
A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459 , 24.8293 ) .
What is population mean?
A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.
Data: 18
for given data
![$$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%5Cbar%7BX%7D%20%26%20%3D%5Cfrac%7B%5Csum%20X%20i%7D%7Bn%7D%20%5C%5C%26%20%3D2448%20%2F%20101%20%5C%5C%26%20%3D24.2376%5Cend%7Baligned%7D%24%24)
as population variance is unknown so we used sample variance
![$$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7DS%5E2%20%26%20%3D%5Cfrac%7B1%7D%7Bn-1%7D%5Cleft%28%5Csum%20X%20i%5E2-n%20%5Ctimes%20%5Cbar%7BX%7D%5E2%5Cright%29%20%5C%5CS%5E2%20%26%20%3D%5Cfrac%7B1%7D%7B100%7D%5Cleft%2860232-101%20%5Ctimes%2024.2376%5E2%5Cright%29%20%5C%5C%26%20%3D8.9830%5Cend%7Baligned%7D%24%24)
Now
![\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cbar%7BX%7D-%5Cmu%7D%7BS%20%2F%20%5Csqrt%7Bn%7D%7D%20%5Csim%20t_%7Bn-1%7D%24%24)
hence 95 % of population mean is
As n=101 which is large so critical value is 1.98397
![$$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%26%20%3D%5Cleft%28%5Cbar%7BX%7D-%5Csqrt%7B%5Cfrac%7BS%7D%7Bn%7D%7D%20%5Ctimes%20t_%7B%28n-1%2C%20%5Calpha%20%2F%202%29%7D%2C%20%5Cbar%7BX%7D%2B%5Csqrt%7B%5Cfrac%7BS%7D%7Bn%7D%7D%20%5Ctimes%20t_%7B%28n-1%2C%20%5Calpha%20%2F%202%29%7D%5Cright%29%20%5C%5C%26%20%3D%5Cleft%2824.2376-%5Csqrt%7B%5Cfrac%7B8.9830%7D%7B101%7D%7D%20%5Ctimes%201.98397%2C24.2376%2B%5Csqrt%7B%5Cfrac%7B8.9830%7D%7B101%7D%7D%20%5Ctimes%201.98397%5Cright%29%20%5C%5C%26%20%3D%2823.6459%2C24.8293%29%5Cend%7Baligned%7D%24%24)
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Answer:uh kinda
Step-by-step explanation:
Answer:
It would be A because to do experimental probability you have to add the total amount out trials and that would be the denominator and the number of times 3 happened would be the numerator.
Answer:
x = (-15)
y = 6
z = 3
Step-by-step explanation:
x + y + z = -6______(1)
2x - y - 5z = -21____(2)
-x - y -6z = -9______(3)
(1) + (2)
![x + y + z + ( - x - y - 6z) = - 6 + ( - 9) \\ x + y + z - x - y - 6z = - 15 \\ - 5z = - 15 \\ z = \frac{ - 15}{ - 5} \\ z = 3 \\](https://tex.z-dn.net/?f=x%20%2B%20y%20%2B%20z%20%20%2B%20%28%20-%20x%20-%20y%20-%206z%29%20%3D%20%20-%206%20%2B%20%28%20-%209%29%20%5C%5C%20x%20%2B%20y%20%2B%20z%20%20-%20%20x%20%20-%20%20y%20-%206z%20%3D%20%20-%2015%20%5C%5C%20%20-%205z%20%3D%20%20-%2015%20%5C%5C%20z%20%3D%20%20%5Cfrac%7B%20-%2015%7D%7B%20-%205%7D%20%20%5C%5C%20z%20%3D%203%20%5C%5C%20)
z = 3, (1) + (2)
![x + y + 3 + (2x - y - 5z) = - 6 + ( - 21) \\ x + y + 3 +( 2x - y - 5( - 3) = - 27 \\ x + y + 3 + (2x - y + 15) = - 27 \\ x + y + 3 + 2x - y + 15 = - 27 \\ 3x + 18 = - 27 \\ 3x = - 27 - 18 \\ 3x = - 45 \\ x = \frac{ - 45}{3} \\ x = ( - 15) \\](https://tex.z-dn.net/?f=x%20%2B%20y%20%2B%203%20%2B%20%282x%20-%20y%20-%205z%29%20%3D%20%20-%206%20%2B%20%20%28%20-%2021%29%20%5C%5C%20x%20%2B%20y%20%2B%203%20%2B%28%202x%20-%20y%20-%205%28%20-%203%29%20%3D%20%20-%2027%20%5C%5C%20x%20%2B%20y%20%2B%203%20%2B%20%282x%20-%20y%20%2B%2015%29%20%3D%20%20-%2027%20%5C%5C%20x%20%2B%20y%20%2B%203%20%2B%202x%20-%20y%20%2B%2015%20%3D%20%20-%2027%20%5C%5C%203x%20%2B%2018%20%3D%20%20-%2027%20%5C%5C%203x%20%3D%20%20-%2027%20%20-%2018%20%5C%5C%203x%20%3D%20%20-%2045%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B%20-%2045%7D%7B3%7D%20%20%5C%5C%20x%20%3D%20%28%20-%2015%29%20%5C%5C%20)
x = (-15), (1)
![x + y + z = - 6 \\ ( - 15) + y + 3 = - 6 \\ - 12 + y = - 6 \\ y = - 6 + 12 \\ y = 6 \\](https://tex.z-dn.net/?f=x%20%2B%20y%20%2B%20z%20%3D%20%20-%206%20%5C%5C%20%28%20-%2015%29%20%2B%20y%20%2B%203%20%3D%20%20-%206%20%5C%5C%20%20-%2012%20%2B%20y%20%3D%20%20-%206%20%5C%5C%20y%20%3D%20%20-%206%20%2B%2012%20%5C%5C%20y%20%3D%206%20%5C%5C%20)