Write an equation of the line that passes through (3, 2)(3, 2) and is perpendicular to the line y=13x−3y=13x−3.
1 answer:
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Let
In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:
So, the base case is ok. Now, we need to assume and prove
.
states that
Since we're assuming , we can substitute the sum of the first n terms with their expression:
Which terminates the proof, since we showed that
as required
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