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 Click to view page 1 of the table Click to view page 2 of the table. -6.2 hours =1.0 hour 3 4 5 6 7 8 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.) (b) Between what two values does the middle 50% of the sleep times lie? The middle 50% of sleep times lies between (Round to two decimal places as needed.) hours on the low end and hours on the high end

Explanation / Answer

Mean is 6.2 and s is 1

a) for 5% , we need to look at the value at 95% , thus the z at 95% is 1.65 from normal distribution table

therefore answer is mean+s*z=6.2+1.65*1=7.85

b) For middle 50% we need P(-X<x<X) or 2*P(x<X)-1=0.5 or P(x<X)=0.75

z for 0.75 is 0.68

thus answer is mean+z*s =6.2+0.68*1=6.88

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