Answer:
Confidence limit = [52.8%, 75.2%]
Step-by-step explanation:
![P=\frac{45}{70}= 0.64](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B45%7D%7B70%7D%3D%200.64)
![(1-P)=1-0.64=0.36](https://tex.z-dn.net/?f=%281-P%29%3D1-0.64%3D0.36)
![n= 70](https://tex.z-dn.net/?f=n%3D%2070)
±
![\sqrt{\frac{P(1-P)}{n} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7BP%281-P%29%7D%7Bn%7D%20%7D)
where the value
will be taken from the z-table for 95% confidence interval
1-0.95= 0.05/2= 0.025
0.95+0.025= 0.0975
From the z-table the value of
corresponding to 0.0975 is 1.96
±
![\sqrt{\frac{0.64*0.36}{70} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B0.64%2A0.36%7D%7B70%7D%20%7D)
±
![(0.057)](https://tex.z-dn.net/?f=%280.057%29)
± ![0.112](https://tex.z-dn.net/?f=0.112)
% ±
%
so the confidence interval is
%
%
![[52.8, 75.2]](https://tex.z-dn.net/?f=%5B52.8%2C%2075.2%5D)
You have to graph the first one so you would do total cost=1.25*lb
Answer:
45
Step-by-step explanation:
They add up to 90, so 90 - 45 = 45 degrees
If an experiment has
possible outputs, each with probability
![P_1,\ P_2,\ldots,\ P_N](https://tex.z-dn.net/?f=%20P_1%2C%5C%20P_2%2C%5Cldots%2C%5C%20P_N%20)
then the sum of all probabilities is always one:
![P_1 + P_2 + \ldots + P_N=1](https://tex.z-dn.net/?f=%20P_1%20%2B%20P_2%20%2B%20%5Cldots%20%2B%20P_N%3D1%20)
So, in your case, you have
![P(\text{grape}) + P(\text{cherry}) + P(\text{orange}) = 1](https://tex.z-dn.net/?f=%20P%28%5Ctext%7Bgrape%7D%29%20%2B%20P%28%5Ctext%7Bcherry%7D%29%20%2B%20P%28%5Ctext%7Borange%7D%29%20%3D%201%20)
plugging in the given values:
![\dfrac{3}{8} + \dfrac{1}{3} + P(\text{orange}) = 1 \iff \dfrac{17}{24} + P(\text{orange}) = 1](https://tex.z-dn.net/?f=%20%5Cdfrac%7B3%7D%7B8%7D%20%2B%20%5Cdfrac%7B1%7D%7B3%7D%20%2B%20P%28%5Ctext%7Borange%7D%29%20%3D%201%20%5Ciff%20%5Cdfrac%7B17%7D%7B24%7D%20%2B%20P%28%5Ctext%7Borange%7D%29%20%3D%201)
we can deduce that
![P(\text{orange}) = 1-\dfrac{17}{24} = \dfrac{7}{24}](https://tex.z-dn.net/?f=%20P%28%5Ctext%7Borange%7D%29%20%3D%201-%5Cdfrac%7B17%7D%7B24%7D%20%3D%20%5Cdfrac%7B7%7D%7B24%7D)