We are given with the principal amount of <span> $1 million and is asked in the problem to calculate for the money supply given the reserve ratio is 15%. The formula that is applicable to this problem is F = P / r where P is the principal amount, r is the ratio and F is the future/ money supply. In this case, upon substitution, F = $1 m million / 0.15 = $6.67 million. The money put into reserve is expected to increase after putting into reserve. The lower the reserve ratio, the higher the money supply will be. Conversely, the higher the principal amount, the higher the money supply.</span>
Answer:
a)
, in which z is related to the confidence level.
b) A sample size of 991 is needed.
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 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)
In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent
This means that ![\pi = 0.16](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.16)
a. What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03 (round up to the next whole number).
This is n for which
. 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)
![0.03 = z\sqrt{\frac{0.16*0.84}{n}}](https://tex.z-dn.net/?f=0.03%20%3D%20z%5Csqrt%7B%5Cfrac%7B0.16%2A0.84%7D%7Bn%7D%7D)
![0.03\sqrt{n} = z\sqrt{0.16*0.84}](https://tex.z-dn.net/?f=0.03%5Csqrt%7Bn%7D%20%3D%20z%5Csqrt%7B0.16%2A0.84%7D)
![\sqrt{n} = \frac{z\sqrt{0.16*0.84}}{0.03}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7Bz%5Csqrt%7B0.16%2A0.84%7D%7D%7B0.03%7D)
![(\sqrt{n})^2 = (\frac{z\sqrt{0.16*0.84}}{0.03})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%28%5Cfrac%7Bz%5Csqrt%7B0.16%2A0.84%7D%7D%7B0.03%7D%29%5E2)
, in which z is related to the confidence level.
Question b:
99% confidence level,
So
, z is the value of Z that has a pvalue of
, so
.
![n = (\frac{z\sqrt{0.16*0.84}}{0.03})^2](https://tex.z-dn.net/?f=n%20%3D%20%28%5Cfrac%7Bz%5Csqrt%7B0.16%2A0.84%7D%7D%7B0.03%7D%29%5E2)
![n = (\frac{2.575\sqrt{0.16*0.84}}{0.03})^2](https://tex.z-dn.net/?f=n%20%3D%20%28%5Cfrac%7B2.575%5Csqrt%7B0.16%2A0.84%7D%7D%7B0.03%7D%29%5E2)
![n = 990.2](https://tex.z-dn.net/?f=n%20%3D%20990.2)
Rounding up
A sample size of 991 is needed.
This seems to be a reflection over the 'y' axis. Notice that the 'x' coordinates of points U and V are x =2 in the original figure, and then, 'x' coordinates of U' and V' are x = -2
All 'y' coordinates for the transformated figure (S'T'U'V'W') are the same that the original figure (STUVW), but the 'x' coordinates are exactly the opposite
This transformation is :
what answer are you talking about you don't know what the question is we don't know what the question is what are you asking do you know the question
Answer:
x = ±√ 1.667 = ± 1.29099
Step-by-step explanation:
p 3and 8
4 5
zeros -8 +1.667