Can someone pls help and ty
2 answers:
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Answer:
0
Step-by-step explanation:
From your problem, we have to extract the information that are important from the first two intregrals so we can solve the double integral.
We also have that:
---------------------------------
With this, now we can solve the double integral.
Since the limits of integration are constant, i can use dA both as dydx or dxdy. I am going to use dydx.
So the double integral will be:
We solve a double integral from the inside to the outside, so the first integral we solve is:
f is a function of x and we are integrating dy, so this means that f is a constant. Our integral now is this:
From above, we have that
So,
Now we have to solve the outside integral:
We know that
So the double integral will be 0
Answer:
And if we solve for a we got
So the value of height that separates the bottom 90% of data from the top 10% is 4.624.
So then the best answer for this case would be:
C. 4.64
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 weights of a population, and for this case we know the distribution for X is given by:
Where and
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 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
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 a we got
So the value of height that separates the bottom 90% of data from the top 10% is 4.624.
So then the best answer for this case would be:
C. 4.64