Question

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?

a) 6
b) 14
c) 19
d) 20
e) 81

Answer 1

c) 19%

Explanation:

80% of the total interns at the hospital receive fewer than 6 hours of sleep.

That means that 20% of the total interns receive 6 or more hours of sleep.

75% of the total interns receive fewer than 6 hours of sleep and report feeling tired during their shifts, which means that 5% of the interns receive fewer than 6 hours of sleep and don't report feeling tired.

70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. This means the 70% of the 20% of interns that receive 6 or more hours of sleep. To find what is the 70% of 20%, we multiply
`20*0.7=14`

14% of the interns receive 6 or more hours of sleep and report no feelings of tiredness.

To find the total percent of interns that report no feelings of tiredness, we sum the 14% of interns who receive 6 or more hours of sleep and report no tiredness, plus the 5% of interns who receive fewer than 6 hours of sleep and report no tiredness. The result is that 19% of the total interns report no feelings of tiredness during their shifts.