What are the coordinates of the3/4point of the way from A(-6, -3)to B(10,9)?
1 answer:
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Answer:
Step-by-step explanation:
Complete question
Required
Solve for x
We have:
Collect like terms
Multiply through by
Make x the subject
Answer:
a)
So the value of height that separates the bottom 75% of data from the top 25% is 236.121.
b)
c)
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".
2) Part a
Let X the random variable that represent the cuts 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 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25
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 75% of data from the top 25% is 236.121.
Part b
For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:
And we want this probability:
We can find the individual probabilities like this:
Part c
For this case we know that the distribution for the sample mean is given by:
And we want this probability:
And for this case we can use the complement rule and the z score given by:
And if we replace we got:
Given:
In triangle ABC, point D is the centroid, and BD = 6.
To find:
The measure of side BE.
Solution:
We know that the centroid divides each median in 2:1.
In the given figure BE is a median and point D is the centroid. It means point D divides the segment BE in 2:1.
Let BD and DE are 2x and x respectively.
We have, BD = 6 units.
Now,
Therefore, the measure of side BE is 9 units.