Which of the following is the quotient of the rational expressions shown below?
2 answers:
The given fraction involves two Rational Expressions, one in numerator and one in denominator.
The rational expression in the denominator can be multiplied to the numerator after taking its reciprocal, this will help to simplify the expression as shown below:
There are no common factors in the numerator and the denominator so the expression cannot be simplified any further.
The rational expression in the denominator can be multiplied to the numerator after taking its reciprocal, this will help to simplify the expression as shown below:
There are no common factors in the numerator and the denominator so the expression cannot be simplified any further.
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Answer:
a)
We want this probability:
And using the z score formula given by:
We got:
b) 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 45.707.
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".
Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
And we want this probability:
And using the z score formula given by:
We got:
We want this probability:
And using the z score formula given by:
We got:
Part b
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 45.707.