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. Click to view page 1 of the table. LOADING... Click to view page 2 of the table. LOADING... 3 4 5 6 7 8 9 10 Bold Sleeping Times of Sleeping Times of Bold Medical Residents Medical Residents mu equals 6.6 hours =6.6 hours sigma equals 1.0 hour =1.0 hour Hours Hours A graph titled "Sleeping Times of Medical Residents" has a horizontal axis labeled "Hours" from 3 to 10 in increments of 1. A normal curve labeled mu = 6.6 hours and sigma = 1.0 hour is over the horizontal axis and is centered on 6.6. (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 nothing 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 nothing hours on the low end and nothing hours on the high end.

Explanation / Answer

a) z score for top 5% of sleeping times = 1.645

Hence,

Shortest time spent sleeping = 6 + 1.65*1 = 7.65

b) z scores for middle 50% of sleep times = -0.67, 0.67

Hence,

Range of middle 50% of sleep times

= (6.6 - 0.67*1, 6.6 + 0.67*1)

= (5.93, 7.27)

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