Question

The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution, with a mean of 6.1 hours and a standard deviation of 1.0 hours. (Source: National Institute of Occupational Safety and Health, Japan)

(a) What is the shortest time spent sleeping that would still place a resident in the top 5% of sleeping times?

(b) Between what two values does the middle 50% of the sleep times lie?

Answer #1

\\Mean (\mu)= 6.1

\\Standard\;Deviation (\sigma)= 1

\\\\ \text{Since we know that}

\\z_{ score } = \frac{x-\mu}{\sigma}

a) Given in the question, top 5% means p = 0.95

b) Given in the question, middle 50% means p = 0.25 to p =
0.75

&

**Middle 50% values lie between 5.4255 &
6.7745**

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.
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Bold Sleeping Times ofSleeping Times of
Bold Medical ResidentsMedical Residents
mu equals 5.7 hoursμ=5.7 hours
sigma equals 1.2 hourσ=1.2 hour
Hours

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