36 Solve for x. 112 0 0
2 answers:
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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.
Answer:
Step-by-step explanation:
If you plot the focus and the directrix on a coordinate plane, because the parabola wraps itself around the focus away from the directrix, we know that this parabola opens to the left. That means its general form is
where h and k are the coordinates of the vertex and p is the distance between the vertex and either the focus or the directrix because both distances are the same. Knowing that both distances are the same, it logically follows that the vertex is directly in between the focus and the directrix. So the vertex is at the origin, (0, 0). p is 2 because the vertex is at an x value of 0 and the directrix is at the x value of 2, and because the focus is at an x value of -2. Filling in the equation, then:
which simplifies to
and, solving for x: