Answer:
We are given that The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees.
Number of Assemblers(x) One-Hour Production(y) (units)
2 11
4 18
1 7
5 29
3 20
a. Draw a scatter diagram.
Solution : Refer the attached figure
b. Based on the scatter diagram, does there appear to be any relationship between the number of assemblers and production? Explain.
Solution: The equation that shows the relationship between the number of assemblers and production is ![y=5.1x+1.7](https://tex.z-dn.net/?f=y%3D5.1x%2B1.7)
Where y is One-Hour Production (units) and x is the Number of Assemblers
c.Compute the correlation coefficient.
Solution:
Formula of correlation coefficient:![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{[n \sum x^2 -(\sum x)^2][n \sum y^2 -(\sum y)^2]}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Bn%20%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%20%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D)
x y xy
![y^2](https://tex.z-dn.net/?f=y%5E2)
2 11 22 4 121
4 18 72 16 324
1 7 7 1 49
5 29 145 25 841
3 20 60 9 400
Sum: 15 85 306 55 1735
n=5
Substitute the values in the formula :
![r=\frac{5(306)-(15)(85)}{[5 (55) -(15)^2][5 (1735) -(85)^2]}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B5%28306%29-%2815%29%2885%29%7D%7B%5B5%20%2855%29%20-%2815%29%5E2%5D%5B5%20%281735%29%20-%2885%29%5E2%5D%7D)
![r=0.00351](https://tex.z-dn.net/?f=r%3D0.00351)
The correlation coefficient is 0.00351
The radius is half the diameter, so the diameter of the circle would be the radius times 2.
1.9*2=3.8
The diameter is 3.8.
Answer: there are 50 humans and 24 horses.
Step-by-step explanation:
Let x represent the number of humans in the horse racing area.
Let y represent the number of horses in the horse racing area.
He counted 74 heads. A human has one head and a horse also has one head. It means that
x + y = 74
He counted 196 legs. A human has 2 legs and a horse has 4 legs. It means that
2x + 4y = 196 - - - - - - - -- - -1
Substituting x = 74 - y into equation 1, it becomes
2(74 - y) + 4y = 196
148 - 2y + 4y = 196
- 2y + 4y = 196 - 148
2y = 48
y = 48/2 = 24
x = 74 - y = 74 - 24
x = 50
The answer to the question is B
Answer: 272
Step-by-step explanation:
Given : A pilot sample of 25 voters found that 21 of them intended to vote in the election.
i.e. ![\hat{p}=\dfrac{21}{25}=0.84](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B21%7D%7B25%7D%3D0.84)
and the voters sampled = 25
Significance level : ![\alpha=1-0.94=0.06](https://tex.z-dn.net/?f=%5Calpha%3D1-0.94%3D0.06)
Critical value : ![z_{\alpha/2}=z_{0.03}1.88](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.03%7D1.88)
Margin of error: E = 0.04
The formula to find the sample size is given by :-
![n=\hat{p}(1-\hat{p})(\dfrac{z_{\alpha/2}}{E})^2\\\\\Rightarrow\ n=0.84(1-0.84)(\dfrac{1.88}{0.04})^2\\\\=296.8896\approx297](https://tex.z-dn.net/?f=n%3D%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%28%5Cdfrac%7Bz_%7B%5Calpha%2F2%7D%7D%7BE%7D%29%5E2%5C%5C%5C%5C%5CRightarrow%5C%20n%3D0.84%281-0.84%29%28%5Cdfrac%7B1.88%7D%7B0.04%7D%29%5E2%5C%5C%5C%5C%3D296.8896%5Capprox297)
Then, the additional voters need to be sample = ![297-25=272](https://tex.z-dn.net/?f=297-25%3D272)
Hence, the region should sample 272 additional voters.