Answer:
![\bar x = 82](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%2082)
![\sigma = 9.64](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%209.64)
Step-by-step explanation:
Given
![n = 12](https://tex.z-dn.net/?f=n%20%3D%2012)
![87\ 91\ 86\ 82\ 72\ 91\ 60\ 77\ 80\ 79\ 83\ 96](https://tex.z-dn.net/?f=87%5C%2091%5C%2086%5C%2082%5C%2072%5C%2091%5C%2060%5C%2077%5C%2080%5C%2079%5C%2083%5C%2096)
Solving (a); Point estimate of mean
To do this, we simply calculate the sample mean
![\bar x = \frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
![\bar x = \frac{87+ 91+ 86+ 82+72+91+60+77+80+79+83+96}{12}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B87%2B%2091%2B%2086%2B%2082%2B72%2B91%2B60%2B77%2B80%2B79%2B83%2B96%7D%7B12%7D)
![\bar x = \frac{984}{12}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B984%7D%7B12%7D)
![\bar x = 82](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%2082)
Solving (b); Point estimate of standard deviation
To do this, we simply calculate the sample standard deviation
![\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n - 1}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%28x-%5Cbar%20x%29%5E2%7D%7Bn%20-%201%7D)
![\sigma = \sqrt\frac{(87-82)^2+ (91-82)^2+ ....+ (79-82)^2+ (83-82)^2+ (96-82)^2}{12-1}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%5Cfrac%7B%2887-82%29%5E2%2B%20%2891-82%29%5E2%2B%20....%2B%20%2879-82%29%5E2%2B%20%2883-82%29%5E2%2B%20%2896-82%29%5E2%7D%7B12-1%7D)
![\sigma = \sqrt\frac{1022}{11}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%5Cfrac%7B1022%7D%7B11%7D)
![\sigma = \sqrt{92.91}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B92.91%7D)
![\sigma = 9.64](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%209.64)
<em>Note that: The sample mean and the sample standard deviation are the best point estimators for the mean and the standard deviation, respectively.</em>
<em>Hence, the need to solve for sample mean and sample standard deviation</em>
Answer:
<h2>Use Desmos!</h2>
Step-by-step explanation:
Just type 10% into the calculator and it will automatically say
" 10% of " then you can type in any number you want to be
ten percent of!
Hope this helps! <3
21 and -14 add to 7 and sum to -294 when multiplied
The answer is A. > because -3 + 7 is -4 and -10 -2 is -12. -4 is greater than -12. good luck!