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2 answers:
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Answer:
Circumference of a circle=
Step-by-step explanation:
The circumference of any circle is the total length of its boundary which can be calculated by the formula:
Circumference of a circle=
Where 'r' is the radius of the circle
For, the given circle the circumference can be find in terms of by putting some value of radius in the formula, which gives the circumference in terms of
.
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.