Answer:
She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
Step-by-step explanation:
We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.
And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.
As we know that the margin of error is given by the following formula;
The margin of error =
Here,
= standard deviation = 3.6 mm
n = sample size of components
= level of significance = 1 - 0.90 = 0.10 or 10%
= 0.05 or 5%
Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.
So, the margin of error =
0.1 mm = ![1.645 \times \frac{3.6}{\sqrt{n} }](https://tex.z-dn.net/?f=1.645%20%5Ctimes%20%5Cfrac%7B3.6%7D%7B%5Csqrt%7Bn%7D%20%7D)
![\sqrt{n} = \frac{3.6\times 1.645}{0.1 }](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%20%5Cfrac%7B3.6%5Ctimes%201.645%7D%7B0.1%20%7D)
= 59.22
n =
= 3507.0084 ≈ 3507.
Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
Best answer to this would be the probability that Christina will choose three action movies can be expressed as 20C3/9C3 .
First we need to write the equations for the given scenario. Using the equations, we can form a system of matrix for the situation.
Let the customer buys, x pounds of almonds, y pounds of cashews and z pounds of walnuts. Since he buys 12 pounds of mixed nuts, we can write:
Total cost of these mixed nuts was $118. So we can write:
![7x+10y+12z=118](https://tex.z-dn.net/?f=7x%2B10y%2B12z%3D118)
Customer buys 2 more pounds of walnut than cashews. So, we can write:
![z=y+2 \\ \\ -y+z=2](https://tex.z-dn.net/?f=z%3Dy%2B2%20%5C%5C%20%20%5C%5C%20%0A-y%2Bz%3D2)
Using these equations, we can set up the system of matrix as shown below in the image.
The system of equations that is represented in the graph is:,y = -2.x-2y =6..Option B is correct.
<h3>What is a graph?</h3>
A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
Two lines may be seen on the graph:
y = -2
The lines pass through (-3) and (6, 0). We use the slope-intercept form to get the second line's equation: y=mx+c
m = 0-(-3)/(6-0)
m=3/6
m=1/2
Substitute the values as;
![\rm y = \frac{1}{2}x+c](https://tex.z-dn.net/?f=%5Crm%20%20y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%2Bc)
For the point x = 0 and y = -3
![\rm y = \frac{1}{2}x-3](https://tex.z-dn.net/?f=%5Crm%20%20y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx-3)
The equation can be written as;
x - 2y = 6
The system of equations that is represented in the graph is:,y = -2.x-2y =6..
Hence, option B is correct.
To learn more about the graph, refer to the link;
brainly.com/question/14375099
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