Find the slope of the graphed line
1 answer:
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Answer:
a. The positive difference between Nelson's height and the population mean is: .
b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).
c. Nelson's z-score: (Nelson's height is <em>below</em> the population's mean 1.174 standard deviations units).
d. Nelson's height is <em>usual</em> since .
Step-by-step explanation:
The key concept to answer this question is the z-score. A <em>z-score</em> "tells us" the distance from the population's mean of a raw score in <em>standard deviation</em> units. A <em>positive value</em> for a z-score indicates that the raw score is <em>above</em> the population mean, whereas a <em>negative value</em> tells us that the raw score is <em>below</em> the population mean. The formula to obtain this <em>z-score</em> is as follows:
[1]
Where
is the <em>z-score</em>.
is the <em>population mean</em>.
is the <em>population standard deviation</em>.
From the question, we have that:
- Nelson's height is 68 in. In this case, the raw score is 68 in
in.
in.
in.
With all this information, we are ready to answer the next questions:
a. What is the positive difference between Nelson's height and the mean?
The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):
.
That is, <em>the positive difference is 2.7 in</em>.
b. How many standard deviations is that [the difference found in part (a)]?
To find how many <em>standard deviations</em> is that, we need to divide that difference by the <em>population standard deviation</em>. That is:
In words, the difference found in part (a) is 1.174 <em>standard deviations</em> from the mean. Notice that we are not taking into account here if the raw score, <em>x,</em> is <em>below</em> or <em>above</em> the mean.
c. Convert Nelson's height to a z score.
Using formula [1], we have
This z-score "tells us" that Nelson's height is <em>1.174 standard deviations</em> <em>below</em> the population mean (notice the negative symbol in the above result), i.e., Nelson's height is <em>below</em> the mean for heights in the club presidents of the past century 1.174 standard deviations units.
d. If we consider "usual" heights to be those that convert to z scores between minus2 and 2, is Nelson's height usual or unusual?
Carefully looking at Nelson's height, we notice that it is between those z-scores, because:
Then, Nelson's height is <em>usual</em> according to that statement.
The another way to state the transformation would be
<u>Solution:</u>
Rotation about the origin at :
The term R0 means that the rotation is about the origin point. Therefore, (R0,180) means that we are rotating the figure to about the origin.
So, the transformation of the general point (x,y) would be (-x,-y) when it is rotated about the origin by an angle of .
Hence according to the representation, the expression would be .