50) Let m be a rational number and n be an irrational number. (m)(n) = c, assume c is rational mn m = c m n = c m , so n is rati
2 answers:
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The answer is: Rational coefficient.
The explanation for this answer is shown below:
1. By definition, a rational number has the form where
is the numerator and
is the denominator. The numerator and the denominator are integers.
2. By definition, integers numbers includes positive numbers, negative numbers and zero.
3. Keeping the information above on mind, you can conclude that the answer is: Rational coefficient.
4. For example:
is a rational coefficient.
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