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

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... 2 3 4 5 6 7 8 9 10 11 Bold Sleeping Times ofBold Medical Residentsmu equals 6.6 hourssigma equals 1.2 hourHours A graph titled "Sleeping Times of Medical Residents" has a horizontal axis labeled "Hours" from 2 to 11 in increments of 1. A normal curve labeled mu = 6.6 hours and sigma = 1.2 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 1 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. ?(Round to two decimal places as? needed.)

Explanation / Answer

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

Hence,

Required hours = 6.6 + 1.645*1.2 = 8.57

b) z score for middle 50% of the data = -0.67, 0.67

Hence,

Middle 50% data lies between (6.6 - 0.67*1.2) and (6.6 + 0.67*1.2) i.e. 5.80 and 7.40

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