Answer:
Step-by-step explanation:
we know that
The volume of a trough is equal to
where
B is the area of equilateral triangle
L is the length of a trough
step 1
Find the area of equilateral triangle B
The area of a equilateral triangle applying the law of sines is equal to
where
substitute
step 2
Find the volume of a trough
we have
substitute
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.
Answer:
Step-by-step explanation:
r = Radius of semicircle =
Area of semicircle is given by
The area of the semicircle is .