The formula for the confidence interval is given by
Sample mean + z*[σ/√n], and
Sample mean - z*[σ/√n]
We have:
Sample mean = 23.95
n = 40
σ = 2.55
z* for 99% confidence = 2.58
Substitute these values into the formula, we have
23.95 + (2.58)(2.55÷√40) = 24.99
23.95 - (2.58)(2.55÷√40) = 22.91
So the lower interval is 22.91 and the highest interval is 24.99
No. when the line reaches 4 on the x axis it is at 13 on the y axis.
Hello,
The formula for finding the area of a circular region is:
![A= \frac{ \alpha *r^{2} }{2}](https://tex.z-dn.net/?f=A%3D%20%20%5Cfrac%7B%20%5Calpha%20%2Ar%5E%7B2%7D%20%7D%7B2%7D%20)
then:
![A_{1} = \frac{80*r^{2} }{2}](https://tex.z-dn.net/?f=A_%7B1%7D%20%3D%20%5Cfrac%7B80%2Ar%5E%7B2%7D%20%7D%7B2%7D%20)
With the two radius it is formed an isosceles triangle, so, we must obtain its area, but first we obtain the height and the base.
![cos(40)= \frac{h}{r} \\ \\ h= r*cos(40)\\ \\ \\ sen(40)= \frac{b}{r} \\ \\ b=r*sen(40)](https://tex.z-dn.net/?f=cos%2840%29%3D%20%5Cfrac%7Bh%7D%7Br%7D%20%20%5C%5C%20%20%5C%5C%20h%3D%20r%2Acos%2840%29%5C%5C%20%5C%5C%20%5C%5C%20sen%2840%29%3D%20%5Cfrac%7Bb%7D%7Br%7D%20%5C%5C%20%5C%5C%20b%3Dr%2Asen%2840%29)
Now we can find its area:
![A_{2}=2* \frac{b*h}{2} \\ \\ A_{2}= [r*sen(40)][r*cos(40)]\\ \\A_{2}= r^{2}*sen(40)*cos(40)](https://tex.z-dn.net/?f=A_%7B2%7D%3D2%2A%20%5Cfrac%7Bb%2Ah%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20A_%7B2%7D%3D%20%5Br%2Asen%2840%29%5D%5Br%2Acos%2840%29%5D%5C%5C%20%20%5C%5CA_%7B2%7D%3D%20r%5E%7B2%7D%2Asen%2840%29%2Acos%2840%29)
The subtraction of the two areas is 100cm^2, then:
Answer: r= 1.59cm