Approximate the solution to the system of equations.
1 answer:
Answer:
a) at x=0.5 y=2 and at x=1 y=2 this similarity in values shows that the solution for x is between 0.5 and 1
c) The x solution will be between x=0.0 and x=0.7 .
There is a similarity in values of y at x=0.6, y=2.4 and at x=0.7 , y=2.4
d) For x= (0.6+0.7)/2 = 1.3/2 =0.65
For y= (2.4+2.3)/2 =4.7/2=2.35
Approximate solution is (0.65, 2.35)
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Answer:
So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.
Step-by-step explanation:
1) 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".
2) Solution to the problem
Let X the random variable that represent the scores on the LSAT of a population, and for this case we know the distribution for X is given by:
Where and
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 0.35 of the area on the left and 0.65 of the area on the right it's z=-0.385. On this case P(Z<-0.385)=0.35 and P(Z>-0.385)=0.65
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 35% of data from the top 65% (Or the 35 percentile) is 146.7.