Answer: a) 683 b) 1067
Step-by-step explanation:
The confidence interval for population proportion is given by :-
![p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}](https://tex.z-dn.net/?f=p%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D)
a) Given : Significance level :![\alpha=1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3D1-0.95%3D0.05)
Critical value : ![z_{\alpha/2}}=\pm1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%7D%3D%5Cpm1.96)
Margin of error : ![E=0.03](https://tex.z-dn.net/?f=E%3D0.03)
Formula to calculate the sample size needed for interval estimate of population proportion :-
![n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.2(0.8)(\dfrac{1.96}{0.03})^2=682.951111111\approx683](https://tex.z-dn.net/?f=n%3Dp%281-p%29%28%5Cdfrac%7Bz_%7B%5Calpha%2F2%7D%7D%7BE%7D%29%5E2%5C%5C%5C%5C%3D0.2%280.8%29%28%5Cdfrac%7B1.96%7D%7B0.03%7D%29%5E2%3D682.951111111%5Capprox683)
Hence, the required sample size would be 683 .
b) If no estimate of the sample proportion is available then the formula to calculate sample size will be :-
![n=0.25(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{1.96}{0.03})^2=1067.11111111\approx1067](https://tex.z-dn.net/?f=n%3D0.25%28%5Cdfrac%7Bz_%7B%5Calpha%2F2%7D%7D%7BE%7D%29%5E2%5C%5C%5C%5C%3D0.25%28%5Cdfrac%7B1.96%7D%7B0.03%7D%29%5E2%3D1067.11111111%5Capprox1067)
Hence, the required sample size would be 1067 .
Scene two because he has more than half of the lines
Answer: This problem is a fraction since we have several equal parts that make up one whole. The problem asks us to talk about the relationship of white pieces to the whole. Since we know the whole is made up of 7 pieces (4 blue parts and 3 white parts = 7 total parts), then 7 will be our denominator (number on the bottom of the fraction).
Now that we have our number on the bottom, we need to look back at the question to carefully decide what parts of the whole we are looking at. The question wants to know how many of the parts are white. We know that 3 of the parts are white, so that is our numerator (number of the top of the fraction).
Our final answer is 3/7 or "three-sevenths." Said another way, three of the seven pieces are white.
Step-by-step explanation:
<span>In the problem, we were asked to find the distance from the base towards the island. First, we need to calculate for theta. So, 90-50 = 40°
Remember mnemonics, SOH CAH TOA. Since given is the angle and the altitude, we are going to use the tangent function.
tan40° = d/500
= 419.54 or approximately 420 feet.
The island is 420 feet away from the location underneath the helicopter.</span>
Answer:
9/16
is already in the simplest form. It can be written as 0.5625 in decimal form (rounded to 6 decimal places).
Step-by-step explanation: