Which of the following describes the correct process for solving the equation 2x + 6 = 22 and arrives at the correct solution? (
2 answers:
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Answer:
A. P(x<3.85 or x>4.15)= P(x<3.85)+P(x>4.15) = 0.1336
Step-by-step explanation:
Working with an ordinary Normal Distribution of probability and trying to find the probabilities asked in it could be difficult, because there´s no easy method to find probabilities in a generic Normal Distribution (with mean μ=4 and STD σ=0.1). The recommended approach to this question is to use a process called "Normalize", this process let us translate the problem of any Normal Distribution to a Standard Normal Distribution (μ=0 and σ=1) where there´s easier ways to find probabilities in there. The "Normalization" goes as follows:
Suppose you want to know P(x<a) of the Normal Distribution you are working with:
P(x<a)=P( (x-μ)/σ < (a-μ)/σ )=P(z<b) ( b=(a-μ)/σ )
Where μ is the mean and σ is the STD of your Normal Distribution. Notice P(z<b) now it´s a probability in a Standard Normal Distribution, now we can find it using the available method to do so. My favorite is a chart (It´s attached to this answer) that contains a lot of probabilities in a Standard Normal Distribution. Let´s solve this as an example
A. We want to find the probability of the cork being defective (P(x<3.85) + P(x>4.15)). Now we find those separated and, then, add them for our answer.
Let´s begin with P(x<3.85), we start by normalizing that probability:
P(x<3.85)= P( (x-μ)/σ < (3.85-4)/0.1 )= P(z<-1.5)
And now it´s time to use the chart, it works like this: If you want P(z<c) and the decimal expansion of c=a.bd... , then:
P(z<c)=(a.b , d)
Where (a.b , d) are the coordinates of the probability in the chart. Keep in mind that will only work with "<" (It won´t work directly with P(z>c)) and we will do some extra work in those cases.
P(z<-1.5) is in the coordinates (-1.5 , 0)
P(z<-1.5)= 0.0668
P(x<3.85)= 0.0668
Now we are looking for P(x>4.15), let´s Normalize it too:
P(x>4.15)=P( (x-μ)/σ < (4.15-4)/0.1 )=P(z>1.5)
But remember the chart only work with "<", so we need to use a property of probability:
P(z>1.5)= 1 - P(z<1.5)
Using the chart:
P(z<1.5)=0.9332 (1.5 , 0)
P(z>1.5)= 1 - 0.9332
P(z>1.5)= 0.0668
P(x>4.15)= 0.0668
And our final answer will be:
P(x<3.85 or x>4.15)= P(x<3.85)+P(x>4.15) = 0.1336
The correct match of each tile of the equation with its solution is:
- n - 13 = - 12 →→→ 1
- n/5 = -1/5 →→→ -1
- n + 15 = - 10 →→→ -25
To match each tile to the correct box, we have to solve the arithmetic operations in the box, then drag the correct tile that matches our answer into the box.
From the image attached below;
1.
n - 13 = - 12
Let us add (+13) to both sides to eliminate (-13), i.e.
n - 13 + 13 = - 12 + 13
n = 1
2.
n/5 = -1/5
multiply both side by 5
n/5 × (5) = -1/5 × (5)
n = -1
3.
n + 15 = - 10
n +15 - 15 = - 10 - 15
n = -25
Learn more about matching each tile to the correct box here:
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