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

Algebra ->  Statistics  -> Describing-distributions-with-numbers -> 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      Log On


   

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) About Me  (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.
7aaa03f4ede8309c9a4c012e61e9af2d
a.
The value $47300 is a standard deviation below the mean
58500-11200=47300
While $69700 is a standard deviation above the mean
58500%2B12000=69700
Between the first deviation below and above the mean, you have 34%2B34=68% of the salary earners within this range.
So we have 68% of staffs earning within this range.

b.
The second standard deviation above the mean is $80900.
$58500%2B11200%2B11200=80900+
We have 50%2B13.5%2B2.5=+97.5% earning below $80900.
Therefore, 100-97.5=+2.5% of the workers earn above this amount.

c.
From the Standard Deviation Rule, the probability is only about %281+-0+.997%29+%2F+2+=+0.0015 that a normal value would be more than 3 standard deviations away from its mean in one direction or the other.
The probability is only 0.0002 that a normal variable would be more than 3.5 standard deviations above its mean. Any more standard deviations than that, and we generally say the probability is approximately zero.

so, answer is:
a.
68% of the workers will earn between $47300 and $69700.
b.
2.5% of workers will earn above $80900

c.
Approximately+0+



Answer by ikleyn(52772) About Me  (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  ( ! )