SOLUTION: I need your help please answer..."Supposed you have numbers 50 and 80 and a corresponding scores of -1 and 2. Is it possible to determine the population mean and standard deviation

Algebra ->  Probability-and-statistics -> SOLUTION: I need your help please answer..."Supposed you have numbers 50 and 80 and a corresponding scores of -1 and 2. Is it possible to determine the population mean and standard deviation      Log On


   

Question 1088887: I need your help please answer..."Supposed you have numbers 50 and 80 and a corresponding scores of -1 and 2. Is it possible to determine the population mean and standard deviation? If so, what are those values? If not, explain why it is impossible." As soon as possible. thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

m = population mean
s = standard deviation
z = z score
x = raw score

The z score formula is
z+=+%28x-m%29%2Fs
If the raw score of 50 corresponds to the z score of -1, then we will have
-1+=+%2850-m%29%2Fs
Let's solve for s to get
-1+=+%2850-m%29%2Fs
-1%2As+=+%28%2850-m%29%2Fs%29%2As
-s+=+50-m
s+=+-%2850-m%29
s+=+-50%2Bm
s+=+m-50 Call this equation (1)

The other raw score of 80 corresponds to 2. So we'll plug z = 2 and x = 80 into the original z score formula
z+=+%28x-m%29%2Fs
2+=+%2880-m%29%2Fs
Then multiply both sides by 's'
2+=+%2880-m%29%2Fs
2s+=+%28%2880-m%29%2Fs%29%2As
2s+=+80-m
Now plug in s = m-50 (see equation (1) above)
2s+=+80-m
2%28m-50%29+=+80-m

At this point, we have an equation with one variable. Let's solve for m
2%28m-50%29+=+80-m
2m-100+=+80-m
2m%2Bm+=+80%2B100
3m+=+180
3m%2F3+=+180%2F3
m+=+60

Now that we know m, we can find s
Go back to equation (1). Plug in m = 60
s+=+m-50
s+=+60-50
s+=+10

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In summary,
m+=+60
s+=+10

So the population mean is 60 and the standard deviation is 10