Answer:
Interval [16.34 , 21.43]
Step-by-step explanation:
First step. <u>Calculate the mean</u>
![\bar X=\frac{(23+18+23+12+13+23)}{6}=18.666](https://tex.z-dn.net/?f=%5Cbar%20X%3D%5Cfrac%7B%2823%2B18%2B23%2B12%2B13%2B23%29%7D%7B6%7D%3D18.666)
Second step. <u>Calculate the standard deviation</u>
![\sigma =\sqrt{\frac{(23-18.666)^2+(18-18.666)^2+(23-18.666)^2+(12-18.666)^2+(13-18.666)^2+(23-18.666)^2}{6}}](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Csqrt%7B%5Cfrac%7B%2823-18.666%29%5E2%2B%2818-18.666%29%5E2%2B%2823-18.666%29%5E2%2B%2812-18.666%29%5E2%2B%2813-18.666%29%5E2%2B%2823-18.666%29%5E2%7D%7B6%7D%7D)
![\sigma=\sqrt\frac{18.783+0.443+18.783+44.435+5.666+18.783}{6}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%5Cfrac%7B18.783%2B0.443%2B18.783%2B44.435%2B5.666%2B18.783%7D%7B6%7D)
![\sigma=\sqrt{17.815}=4.22](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B17.815%7D%3D4.22)
As the number of data is less than 30, we must use the t-table to find the interval of confidence.
We have 6 observations, our level of confidence DF is then 6-1=5 and we want our area A to be 80% (0.08).
We must then choose t = 1.476 (see attachment)
Now, we use the formula that gives us the end points of the required interval
![\bar X \pm t\frac{\sigma}{\sqrt n}](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Cpm%20t%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%20n%7D)
where n is the number of observations.
The extremes of the interval are then, rounded to the nearest hundreth, 16.34 and 21.43
Answer:
22, 29, 37
Step-by-step explanation:
There is a pattern to find the next number in the sequence. The sequence is taking the previous number and adding the number it is in the sequence.
Notice how the first number being added is the number of the previous sum and the second number being added is always increasing by one
1+0=1
1+1=2
2+2=4
4+3=7
7+4=11
11+5=16
16+6=22
22+7=29
29+8=37
22, 29, 37
X+5 ≤ -17
Or if it’s y instead of x put that.
Hope this helps though