It should be rational
hope it helps
Answer: 2285
Step-by-step explanation:
Formula to find the sample size is given by :-
![n=p(1-p)(\dfrac{z_c}{E})^2](https://tex.z-dn.net/?f=n%3Dp%281-p%29%28%5Cdfrac%7Bz_c%7D%7BE%7D%29%5E2)
, where p = prior estimate of population proportion.
E= Margin of error.
= z-value for confidence interval of c.
Given : Confidence interval : 95%
From the z-value table , the z-value for 95% confidence interval = ![z_c=1.96](https://tex.z-dn.net/?f=z_c%3D1.96)
The General Social Survey reported a sample where about 61% of US residents thought marijuana should be made legal.
i.e. the prior estimate of population proportion of US residents thought marijuana should be made legal : p=0.61
[∵ sample proportion is the best estimate for population proportion.]
Margin of error : E= 2%=0.02
Now, the required minimum sample size would be :-
![n=0.61(1-0.61)(\dfrac{1.96}{0.02})^2](https://tex.z-dn.net/?f=n%3D0.61%281-0.61%29%28%5Cdfrac%7B1.96%7D%7B0.02%7D%29%5E2)
Simplify ,
![n=0.2379\times9604=2284.7916\approx2285](https://tex.z-dn.net/?f=n%3D0.2379%5Ctimes9604%3D2284.7916%5Capprox2285)
Thus , we need to survey <u>2285</u> Americans .
60/125 so that can be simplified in 12/25, so the percentage is 0.48%
Let the numbers be x and 4x. So, according to the question,
x + 4x = 100
=> 5x = 100
=> x = 100/5
=> x = 20
So, the number are,
x = 20
and
4x = 4×20 = 80
So, the two numbers are 20 and 80.