mirantdon wrote:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during
their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of
tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no
feelings of tiredness during their shifts?
6 14 19 20 81
please help
Whenever we have groups (in this case, interns who get fewer than 6 hours sleep and those who get 6 hours or more) that are being divided into smaller groups (in this case, interns who are tired and those who are not), we can use a
group grid to organize the data. Here's what the grid looks like:
_______________<6______6plus_______Total
tired:
not tired:
total:
In the grid above, every row has to add up to the total, as does every column.
Looking at the top row, interns who get fewer than 6 hours sleep and are tired + those who get 6plus hours sleep and are tired = total tired.
Looking at the left-most column, interns who get fewer than 6 hours sleep and are tired + interns who get fewer than 6 hours and are not tired = total who get fewer than 6 hours sleep.
Now let's fill in the data step by step. Whenever we have 2 entries in a row or column, we can determine the remaining entry, since everything has to add up horizontally and vertically. Let's plug in 100 for the total number of interns:
_______________<6______6plus_______Total
tired:
not tired:
total:_______________________________100
75% of the interns receive fewer than 6 hours of sleep and report feeling tired:
__________________<6______6plus_______Total
tired:________________75
not tired:
total:____________________________________100
80% of the interns receive fewer than 6 hours of sleep:
__________________<6______6plus_______Total
tired:______________75
not tired:___________5
total:______________80_______20________ 100
70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness:
__________________<6______6plus_______Total
tired:______________75_______6__________81
not tired:____________5_______14_________19
total:______________70_______20________ 100
Notice that everything adds up horizontally and vertically.
Total not tired = 19.
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