A circle has a diameter of
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I'll assume you're supposed to compute the line integral of over the given path
. By the fundamental theorem of calculus,
so evaluating the integral is as simple as evaluting at the endpoints of
. But first we need to determine
given its gradient.
We have
Differentiating with respect to gives
and we end up with
for some constant . Then the value of the line integral is
.
Answer:
And if we solve for a we got
So the value of height that separates the bottom 99% of data from the top 1% is 112.92.
So then the player need to score 112.92 or more in order to achieve the requirement.
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 scores of a population, and for this case we know the distribution for X is given by:
Where and
We can solve this problem using the z score formula 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 0.99 of the area on the left and 0.01 of the area on the right it's z=2.33. On this case P(Z<2.33)=0.99 and P(z>2.33)=0.051
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 99% of data from the top 1% is 112.92.
So then the player need to score 112.92 or more in order to achieve the requirement.