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healthcare statistics problem

Lspencer2121

New member
Aug 26, 2013
5
I need help setting this problem up.

6 out of 10 patients discharged in 3 days or less, 12,000 admissions, determine how many were hospitalized over 3 days.

Thanks for the help.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
If 6 out of 10 patients are discharged in 3 days or less, then how many out of ten are hospitalized for more than 3 days?
 

Lspencer2121

New member
Aug 26, 2013
5
I appreciate the help but I am still clueless. I know 6/10 is a ratio, which would convert to 3/5, converts to 0.6. My thought is 0.6/12000 Am I correct?

Thanks again for the help.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
If 6 out of 10 patients are discharged in 3 days or less, then 4 out of ten are hospitalized for more than 3 days.

This comes from the fact that 10 out of 10 are either discharged in 3 days or less or are hospitalized for more than 3 days. These two conditions cover everyone. So, if we let $x$ be the number out of ten that are hospitalized for more than 3 days, we must have:

\(\displaystyle 6+x=10\)

\(\displaystyle x=4\)

In a total of 12,000 admissions, there are 1200 groups of 10. In each of these 1200 groups, 4 of the 10 will have been hospitalized for more than 3 days. So, we have 1200 groups of 4...how many is this?
 

Lspencer2121

New member
Aug 26, 2013
5
Thank you! 4800.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Thank you! 4800.
Yes, that's correct! (Sun)

Another way to look at it is since 60% are discharged in 3 days or less, then we know 40% are hospitalized for more than 3 days, and 40% of 12000 is:

\(\displaystyle 40\%\cdot12000=\frac{40}{100}\cdot12000=40\cdot120=4800\)