Answer:
$28
Step-by-step explanation:
Given:
data = [22,30,35,25,25,20,27]
For eight night, the new list is:
new_data = [22,30,35,25,25,20,27,x]
Mean = 26.50
Mean Formula:
![\displaystyle \large{m=\dfrac{x_1+x_2+x_3+...+x_n}{n} }](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bm%3D%5Cdfrac%7Bx_1%2Bx_2%2Bx_3%2B...%2Bx_n%7D%7Bn%7D%20%7D)
Therefore:
![\displaystyle \large{26.50=\dfrac{22+30+35+25+25+20+27+x}{8}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B26.50%3D%5Cdfrac%7B22%2B30%2B35%2B25%2B25%2B20%2B27%2Bx%7D%7B8%7D%7D)
Multiply both sides by 8:
![\displaystyle \large{26.50\cdot 8=\dfrac{22+30+35+25+25+20+27+x}{8} \cdot 8}\\\displaystyle \large{212=22+30+35+25+25+20+27+x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B26.50%5Ccdot%208%3D%5Cdfrac%7B22%2B30%2B35%2B25%2B25%2B20%2B27%2Bx%7D%7B8%7D%20%5Ccdot%208%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B212%3D22%2B30%2B35%2B25%2B25%2B20%2B27%2Bx%7D)
Solve for x:
![\displaystyle \large{212=22+30+35+25+25+20+27+x}\\\displaystyle \large{212=184+x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B212%3D22%2B30%2B35%2B25%2B25%2B20%2B27%2Bx%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B212%3D184%2Bx%7D)
Subtract 184 both sides:
![\displaystyle \large{212-184=184+x-184}\\\displaystyle \large{28=x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B212-184%3D184%2Bx-184%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B28%3Dx%7D)
Therefore, she will earn $28 in eighth night
The attachment below is the result of combining all eighth data as we get 26.5 through python language with numpy package.