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Answer:
And if we solve for we got
So then the mean is for this case.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.85 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.85
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for we got
So then the mean is for this case.
Answer:
4 + (or -) 3i
Step-by-step explanation:
Hi!
Alright, so we're going to move all of the variables and constants to one side. Then, using the quadratic formula, we'll find the answer.
1. Move 12x-5 to the left side of the equation by
a. Subtracting 12x from both sides
b. adding 5 to both sides.
1: x^2+4x+20-12x+5
2. Group the common terms
x^2+4x-12x+20+5 --> x^2-8x+25
3. Look at the problem. We can't factor this.
Explanation for why this isn't factorable (you can skip this)
(1) 25 is positive, so its two factors will both be either positive or negative. We're looking for a negative 8, so let's go with negative.
(2) Factors of 25: 1 & 25, 5 &5
Seeing the problem? Ya, none of the factors of 25 sum to eight. So, instead, we're going to use the quadratic formula.
4. So, the quadratic formula:
Our equation is x^2-8x+25=0
a is the constant in front of the x^2
b is the constant in front of the x
c is the term without any x values
so, a=1, b=-8, and c= 25
Into equation:
=
=
8/2 = 4
sqrt(-36) = 6i
6i/2 = 3i (remember, we still have the two in the denominator)
4 + (or -) 3i
The intensity of an earthquake with a magnitude of 2 is 100 times greater than the intensity of an a standard earthquake .
<h3>What is magnitude of earthquake?</h3>
Magnitude of earthquake is the measure of the size of origin of the earthquake. The magnitude of the earthquake keeps the same value for each place.
An earthquake with a magnitude of about 2. 0 or less is called a micro-earthquake and not felt usually.The intensity of an earthquake with a magnitude of 2.
Let the intensity of this earthquake is <em>n </em>times greater than the intensity of an a standard earthquake. Thus the intensity of standard earthquake can be given as,
If the magnitude would be 3 then the intensity would be,
It would be 1000 times greater than the standard earthquake and so on.
Thus, the intensity of an earthquake with a magnitude of 2 is 100 times greater than the intensity of an a standard earthquake .
Learn more about the magnitude of earthquake here;