What is the product or (m+3)(M-3)
1 answer:
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Answer:
And then we can conclude that the middle 75% values of her lap times are from a=126.835 to b=132.585
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 times of a population, and for this case we know the distribution for X is given by:
Where and
Since we want the middle 75% values then on tha tails we need 1-0.75 =0.25 or 25% of the data and since the distribution is symmetric we need 12.5 % of the values on each tail.
For this part we want to find a value a and b, such that we satisfy this condition:
(a)
(b)
We can use the z score formula in order to find the value a and b given by:
As we can see on the figure attached the z value that satisfy the condition (b) with 0.125 of the area on the left and 0.875 of the area on the right it's z=-1.15. On this case P(Z<-1.15)=0.125 and P(z>-1.15)=0.875
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 12.5% of data from the top 87.5% is 126.835.
As we can see on the figure attached the z value that satisfy the condition (b) with 0.875 of the area on the left and 0.125 of the area on the right it's z=1.15. On this case P(Z<1.15)=0.875 and P(Z>1.15)=0.125
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
And then we can conclude that the middle 75% values of her lap times are from a=126.835 to b=132.585
Answer:
Step-by-step explanation:
Let's start by identifying relevant angle theorems for two parallel lines cut by a transversal.
Alternate Interior Angles Theorem
Two angles that are on different sides of the transversal and inside of the two parallel lines are congruent (=).
Alternate Exterior Angles Theorem
Two angles that are on different sides of the transversal and outside of the two parallel lines are congruent (=).
Same-side Interior Angles Theorem
Two angles that are on the same side of the transversal and inside of the two parallel lines are supplementary (= 180).
Same-side Exterior Angles Theorem
Two angles that are on the same side of the transversal and outside of the two parallel lines are supplementary (=180).
Corresponding Angles Theorem
Two angles on a figure that correspond are congruent (=).
_
Now, let's look at the figure and apply these theorems.
and
are same-side exterior angles, meaning they're supplementary:
Subtract from both sides of the equation:
Now that we know our value, let's recognize that
(
)corresponds to
, meaning they're congruent:
Subtract from both sides of the equation:
Let's find the value of the angle:
Add:
Since the corresponding angles are of the same value, they're congruent, proving our &
values correct.
_
Since and the angle represented by the expression
(
°) are alternate-interior angles, they are congruent: