The answer is the first one
Comment if you need a better explanation :)
Answer:
The 95% confidence interval is ![0.3795 < p < 0.4405](https://tex.z-dn.net/?f=0.3795%20%3C%20p%20%20%3C%200.4405)
Step-by-step explanation:
From the question we are told that
The sample size is ![n = 1000](https://tex.z-dn.net/?f=n%20%20%3D%20%201000)
The number of approved loan is k = 410
Generally the sample proportion is mathematically represented as
![\r p = \frac{k}{n}](https://tex.z-dn.net/?f=%5Cr%20p%20%20%3D%20%20%5Cfrac%7Bk%7D%7Bn%7D)
substituting values
![\r p = \frac{410}{1000}](https://tex.z-dn.net/?f=%5Cr%20p%20%20%3D%20%20%5Cfrac%7B410%7D%7B1000%7D)
![\r p = 0.41](https://tex.z-dn.net/?f=%5Cr%20p%20%20%3D%200.41)
Given that the confidence level is 95% then the level of significance is mathematically represented as
![\alpha = 100 - 95](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%20100%20-%2095)
![\alpha = 5\%](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%205%5C%25)
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%200.05)
Next we obtain the critical value of
from the normal distribution table,the value is
![Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3DZ_%7B%5Cfrac%7B0.05%20%7D%7B2%7D%20%7D%3D%20%201.96)
Generally the margin of error is mathematically represented as
![E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p(1- \r p)}{n} }](https://tex.z-dn.net/?f=E%20%20%3D%20%20Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%2A%20%5Csqrt%7B%5Cfrac%7B%5Cr%20p%281-%20%5Cr%20p%29%7D%7Bn%7D%20%7D)
substituting values
![E = 1.96 * \sqrt{\frac{ 0.41(1- 0.41)}{1000} }](https://tex.z-dn.net/?f=E%20%20%3D%20%201.96%20%2A%20%5Csqrt%7B%5Cfrac%7B%200.41%281-%200.41%29%7D%7B1000%7D%20%7D)
![E = 0.03048](https://tex.z-dn.net/?f=E%20%20%3D%20%20%200.03048)
The 95% confidence interval for p is mathematically represented as
![\r p - E < p < \r p + E](https://tex.z-dn.net/?f=%5Cr%20p%20%20-%20%20E%20%3C%20p%20%20%3C%20%5Cr%20p%20%20%2B%20%20E)
substituting values
![0.41 - 0.03048 < p < 0.41 + 0.03048](https://tex.z-dn.net/?f=0.41%20-%20%200.03048%20%3C%20p%20%20%3C%200.41%20%2B%20%200.03048)
![0.3795 < p < 0.4405](https://tex.z-dn.net/?f=0.3795%20%3C%20p%20%20%3C%200.4405)
Answer:
(x, y) = (18, 5)
Step-by-step explanation:
Assuming the three lines meet at a single point at lower left (the figure is sloppily drawn), the angle (3x)°+49° is a corresponding angle to (7x-23)°. That means they have the same measure:
3x +49 = 7x -23
72 = 4x . . . . . . . . . add 23-3x
18 = x . . . . . . . . . . . divide by 4
__
Angles (3x)° and (11y-1)° are "corresponding" angles, so are congruent.
3x = 11y -1
3(18) +1 = 11y . . . . add 1, fill in the value of x
55/11 = y = 5 . . . . divide by 11
The values of x and y are 18 and 5, respectively.
Answer: (A1+A2) × B1
Step-by-step explanation:
Here, at first we have two values that are
and ![A_2](https://tex.z-dn.net/?f=A_2)
And, when we add these values we get = ![( A_1 + A_2)](https://tex.z-dn.net/?f=%28%20A_1%20%2B%20A_2%29)
Now when we multiply
by ![B_1](https://tex.z-dn.net/?f=B_1)
We get, ![( A_1 + A_2) . B_2](https://tex.z-dn.net/?f=%28%20A_1%20%2B%20A_2%29%20.%20B_2)
Thus, third Option is correct.
Answer: a: is 10
b is 3
c is 7
d is 0
and e is 2/7
Step-by-step explanation: