The expression 1/4y+3/8 factored is
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:
<h2>D. (-1, -3)</h2>Step-by-step explanation:
Answer:
a) There is outlier (lower category), but this outlier seem certain to be due to an error.
b) There is outlier (upper category), this outlier seem certain to be conceivably correct.
Step-by-step explanation:
a) The outlier in the rock weight is certain to be due to an error. As shown, the rock was weighed five time to ascertain the actual weight or perhaps to known the mean weight. <em>Thus, having a value 4.91 can not be true. It can only be due to an error of recording the values.</em> It suppose to be recorded as 49.1.
b) Since this was a sample of annual income of five different families, it quite possible that a particular family annual income is $1, 200, 000. Hence, we cannot regard this outlier an error, rather conceivably true.
See attached for the box plot of the two data sets.
