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.
mu equals 5.4 hours sigma equals 1.2 hour
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 = 1.2 hour is over the horizontal axis and is centered on 5.4.
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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 __ hours on the low end and __ hours on the high end. ​(Round to two decimal places as​ needed.)

Answer 1

from Z-table, Lookup fro Z-value corresponding to area 0.05 to the right of the normal curve.

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Assume the mean to be symmetrically distributed

from Z-table, Lookup fro Z-value corresponding to area 0.25 to the left of the normal curve.

from Z-table, Lookup fro Z-value corresponding to area 0.25 to the right of the normal curve.

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