SOLUTION: I am having trouble on a problem from my homework assignment. This is the question word for word from the text book:
The average earnings of year-round full-time workers 25-34 y
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Question 1191028: I am having trouble on a problem from my homework assignment. This is the question word for word from the text book:
The average earnings of year-round full-time workers 25-34 years old with a bachelor's degree or higher were $58,500 in 2003. If the standard deviation is $11,200, what can you say about the percentage of these workers who earn;
a. between $47,300 and $69,700?
b. More than $80,900?
c. How likely is it that someone earns more than $100,000?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
The standard normal distribution curve in the attached graph is used to solve this question.
a.
The value $ is a standard deviation below the mean
While $ is a standard deviation above the mean
Between the first deviation below and above the mean, you have % of the salary earners within this range.
So we have % of staffs earning this range.
b.
The second standard deviation above the mean is $.
$
We have % earning below $.
Therefore, % of the workers earn this amount.
c.
From the Standard Deviation Rule, the probability is only about that a normal value would be more than standard deviations away from its in one direction or the other.
The probability is only that a normal variable would be more than standard deviations above its mean. Any more standard deviations than that, and we generally say the probability is approximately .
so, answer is:
a.
% of the workers will earn between $ and $.
b.
% of workers will earn above $
c.
Approximately
Answer by ikleyn(52775) (Show Source): You can put this solution on YOUR website!
.
The normal distribution curve is a bell shaped curve.
These questions are to determine the areas under the normal distribution curve
below the given score; or between two given scores; or above the given score.
It can be done in different ways:
- manually, or
- using online calculator, or
- using your pocket calculator.
MANUALLY
To do it manually, use this Table representing AREA to the LEFT of the Z-score
https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf
USING ONLINE CALCULATOR
To do it using an online (free of charge) calculator, go to this web-site
https://onlinestatbook.com/2/calculators/normal_dist.html
Input the given parameters of each question into an appropriate window of the calculator and get the answers
to your questions.
The calculator has perfect description and design, so EVERY person, even beginner, may work with it on his or her own,
even having minimum knowledge on the subject.
USING YOUR POCKET CALCULATOR
On how to use it, see a text description in THIS Internet source / site
https://mathbits.com/MathBits/TISection/Statistics2/normaldistribution.htm
Or see these Youtube video-lessons
https://www.youtube.com/watch?v=bVdQ7OzGvU0 (for Casio fx-991 MS)
https://www.youtube.com/watch?v=yYpMkgB20C4 (for TI-83 or TI-84 calculators)
Find there EVERYTHING you need to know in clear and compact form.
After learning it, you will be able to solve this problem (and thousand other similar and different problems) ON YOUR OWN,
without asking for help from outside.
Happy learning ( ! )
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