stats question

almill21

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i haven't got a clue on how to solve this... I missed a couple lectures... would appreciate if anyone could help solve the problem with correct solution so that I can verify when i try on my own and so that I can solve the rest of questions like these... [h=1] If the income in a community is normally distributed with a mean of $19,500 and a standard deviation of $1,000 what minimum income does a member of the community have to earn in order to be in the top 10%? What is the maximum one can have and still be in the middle 50%? please show all steps [/h]
 
i haven't got a clue on how to solve this... I missed a couple lectures... would appreciate if anyone could help solve the problem with correct solution so that I can verify when i try on my own and so that I can solve the rest of questions like these... If the income in a community is normally distributed with a mean of $19,500 and a standard deviation of $1,000 what minimum income does a member of the community have to earn in order to be in the top 10%? What is the maximum one can have and still be in the middle 50%? please show all steps
We don't like to "give answers," but if you show us your work we will check your results.

You have tables (surely!) of the cumulative normal distribution. That is, if you make a sketch of the bell cirve, draw a vertical line somewhere, and shade all of the area under the curve to the left of that point you will have F(x). Look into your table to find where F = 0.90 - the remaining area above that will be the highest 10% of the distribution. The x at that point (or it may be called "z") is the number of standard deviations above the mean. The corresponding income is $19,500 + x*($1000.00).

The "middle 50%" includes all the area from F(x) = 0.25 to F(x) = 0.75. Because the curve is symmetric about the mean, you just need to use the table to find x such that F(x) = 0.75. Theat will be the makimum point of the "middle 50%".
 
i haven't got a clue on how to solve this... I missed a couple lectures... would appreciate if anyone could help solve the problem with correct solution so that I can verify when i try on my own and so that I can solve the rest of questions like these... If the income in a community is normally distributed with a mean of $19,500 and a standard deviation of $1,000 what minimum income does a member of the community have to earn in order to be in the top 10%? What is the maximum one can have and still be in the middle 50%? please show all steps
Do you know the topics you missed due to your absence? Do you know z-distribution?
 
showing my work

We don't like to "give answers," but if you show us your work we will check your results.You have tables (surely!) of the cumulative normal distribution. That is, if you make a sketch of the bell cirve, draw a vertical line somewhere, and shade all of the area under the curve to the left of that point you will have F(x). Look into your table to find where F = 0.90 - the remaining area above that will be the highest 10% of the distribution. The x at that point (or it may be called "z") is the number of standard deviations above the mean. The corresponding income is $19,500 + x*($1000.00).The "middle 50%" includes all the area from F(x) = 0.25 to F(x) = 0.75. Because the curve is symmetric about the mean, you just need to use the table to find x such that F(x) = 0.75. Theat will be the makimum point of the "middle 50%".
I have the standard normal probabilities table. so my answer for part A is 19500+1.2(1000)=20700 can you confirm is this correct? thank you
 
soirry I meant to say 19500+1.29(1000)=20790
That is essentially correct. The minimum salary in the upper 10% is very close to $20,790.

Rounding the x from the table would be 1.28 instead of 1.29, or interpolation gives 1.282, so that a slightly more precise result would be $20,782.
 
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