Answer:
Step-by-step explanation:
11
Answer:
The sample size required is 910.
Step-by-step explanation:
The confidence interval for population proportion is:
![CI=\hat p\pm z_{ \alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }](https://tex.z-dn.net/?f=CI%3D%5Chat%20p%5Cpm%20z_%7B%20%5Calpha%20%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%20%7D)
The margin of error is:
![MOE=z_{ \alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }](https://tex.z-dn.net/?f=MOE%3Dz_%7B%20%5Calpha%20%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%20%7D)
Given:
![\hat p = 0.16\\MOE= 0.02\\Confidence\ level =0.90](https://tex.z-dn.net/?f=%5Chat%20p%20%3D%200.16%5C%5CMOE%3D%200.02%5C%5CConfidence%5C%20level%20%3D0.90)
The critical value of <em>z</em> for 90% confidence level is:
*Use a standard normal table.
Compute the sample size required as follows:
![MOE=z_{ \alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }\\0.02=1.645\times \sqrt{\frac{0.16(1-0.16)}{n} }\\n=\frac{(1.645)^{2}\times 0.16\times (1-0.16)}{(0.02)^{2}} \\=909.2244\\\approx910](https://tex.z-dn.net/?f=MOE%3Dz_%7B%20%5Calpha%20%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%20%7D%5C%5C0.02%3D1.645%5Ctimes%20%5Csqrt%7B%5Cfrac%7B0.16%281-0.16%29%7D%7Bn%7D%20%7D%5C%5Cn%3D%5Cfrac%7B%281.645%29%5E%7B2%7D%5Ctimes%200.16%5Ctimes%20%281-0.16%29%7D%7B%280.02%29%5E%7B2%7D%7D%20%5C%5C%3D909.2244%5C%5C%5Capprox910)
Thus, the sample size required is 910.
Answer:
The radius of circle is 3
Step-by-step explanation:
Given the endpoints of diameter of a circle are (6,2) and (0,2)
We know that the equation of circle is
+
= ![r^{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D)
where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.
To find (h,k): the center is midpoint of diameter
Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by
(
,
)
(
,
)
(3, 2)
Hence (h,k) is (3,2)
Substituting values of (h.k) and (x.y) as (3,2) and (0,2) respectively, we get
+
= ![r^{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D)
= ![3^{2}](https://tex.z-dn.net/?f=3%5E%7B2%7D)
r =3
Hence the radius of the circle is 3
Answer:
1,687,500,000,000
Step-by-step explanation:
1) 270,000,000 x 6250