he average time spent sleeping? (in hours) for a group of medical residents at a
ID: 2947031 • Letter: H
Question
he 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.
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Bold Sleeping Times ofSleeping Times of
Bold Medical ResidentsMedical Residents
mu equals 5.4 hours?=5.4 hours
sigma equals 1.3 hour?=1.3 hour
HoursHours
?(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.
he 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...
12345678910Bold Sleeping Times ofSleeping Times of
Bold Medical ResidentsMedical Residents
mu equals 5.4 hours?=5.4 hours
sigma equals 1.3 hour?=1.3 hour
HoursHours
A graph titled "Sleeping Times of Medical Residents" has a horizontal axis labeled "Hours" from 1 to 10 in increments of 1. A normal curve labeled mu = 5.4 hours and sigma = 1.3 hour is over the horizontal axis and is centered on 5.4.Explanation / Answer
a)for top 5% ; at 95th percentile critical z =1.645
hence corresponding value =mean+z*std deviaiton =5.4+1.645*1.3=7.54
b)
for middle 50% values critical z =-/+0.67
hence lower value =mean+z*std deviaiton =5.4-0.67*1.3=4.53
upper value =mean+z*std deviaiton =5.4+0.67*1.3=6.27
The middle? 50% of sleep times lies between 4.53 hours on the low end and 6.27 hours on the high end.
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