The average time spent sleeping (in hours) for a group of medical residents at a

Question

The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution, as shown in the graph to the right. Answer parts (a) and (b) below Sleeping Times of Medical Residents = 5.5 hours = 1.2 hour 9 10 Hours (a) what is the shortest time spent sleeping that would still place a resident in the top 5% of sleeping times? Residents who get at least hours of sleep are in the top 5% of sleeping times. (Round to two decimal places as needed.)

Explanation / Answer

z = (X-Mean)/SD
a) Top 5% is represented by 0.0500 area in the extreme right tail of the normal curve.
The z value which separates this area from the remaining is + 1.645
1.645 = (X - 5.5)/1.2
1.974 = X - 5.5
X = 1.974 +5.5
X = 7.474
= 7.47

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