490 x 2/5 = 980/5 = 196 girls at Garland
945 x 5/7 = 4725/7 = 675 girls at Bowood
Bowood has more girls:
675-196 = 479 more
I need to see more of the picture
Answer:
14 years
Step-by-step explanation:
£280 is 7% of 4000 so £4000 euro more would be 4000/280 = 14
Answer:
We need a sample size of at least 1161.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
The margin of error for the interval is:
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
For this problem, we have that:
![\pi = 0.22](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.22)
90% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
How large a sample should she take?
We need a sample size of at least n.
n is found when ![M = 0.02](https://tex.z-dn.net/?f=M%20%3D%200.02)
So
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![0.02 = 1.645\sqrt{\frac{0.22*0.78}{n}}](https://tex.z-dn.net/?f=0.02%20%3D%201.645%5Csqrt%7B%5Cfrac%7B0.22%2A0.78%7D%7Bn%7D%7D)
![0.02\sqrt{n} = 1.645\sqrt{0.22*0.78}](https://tex.z-dn.net/?f=0.02%5Csqrt%7Bn%7D%20%3D%201.645%5Csqrt%7B0.22%2A0.78%7D)
![\sqrt{n} = \frac{1.645\sqrt{0.22*0.78}}{0.02}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.645%5Csqrt%7B0.22%2A0.78%7D%7D%7B0.02%7D)
![(\sqrt{n})^{2} = (\frac{1.645\sqrt{0.22*0.78}}{0.02})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E%7B2%7D%20%3D%20%28%5Cfrac%7B1.645%5Csqrt%7B0.22%2A0.78%7D%7D%7B0.02%7D%29%5E%7B2%7D)
![n = 1160.88](https://tex.z-dn.net/?f=n%20%3D%201160.88)
Rounding up
We need a sample size of at least 1161.