Question 615703: Hi, i really need help on this question
Goverment wants to give tax breaks to the 15% of population with the lowest salary, the mean salary is normally distributed with $42150 and std. dev of $4530
a. the cut-off margin of income to be eligible for the tax break?
b. the minimum income of 5% of the population with highest income.
c. the percentage of population with income between $30,000 and $70,000.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'll give you the short answer first.
this short answer uses the following normal distribution calculator.
http://davidmlane.com/normal.html
your mean is 42150
your standard deviation is 4530
bottom 15% of the population makes less than 37454.
see picture 1 to see what the inputs and outputs were to get this value.
picture 1
top 5% of the population makes more than 49602.
see picture 2 to see what the inputs and outputs were to get this value.
picture 2
percentage of population with income between 30,000 and 70,000 is equal to 0.9963.
see picture 3 to see what the inputs and outputs were to get this value.
picture 3
this doesn't show you how to get these values through the use of the normal distribution tables.
that's another story.
i have written some lessons on how to use the calculator i used to show you the results.
i have also written some lessons on z-scores and how to use the z-score tables.
the links to those lessons are shown below:
what you are asking is not simple to answer because there's a lot of knowledge about z-scores and how to use the z-score tables that goes into finding the answer.
you have to know how to find the area under the curve given the z-score.
you also have to know how to find the z-score given the area under the curve.
the tool i used takes a lot of the work out of that and is very convenient to use but not useful if you are forced to use the tables because your instructor wants you to learn how to use them.
this tool can work off the direct data as i did, or it can work off the z-scores which is another lesson in itself.
read the lessons and come back to me with more questions if you have them.
best i can do for now.
the lessons:
manually using a z-table
z-scores and the z-table calculator
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