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

ID: 3062130 • Letter: T

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.

Bold Sleeping Times ofSleeping Times of

Bold Medical ResidentsMedical Residents

mu equals 6.4 hours=6.4 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.)

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Bold Sleeping Times ofSleeping Times of

Bold Medical ResidentsMedical Residents

mu equals 6.4 hours=6.4 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 2 to 11 in increments of 1. A normal curve labeled mu = 6.4 hours and sigma = 1.3 hour is over the horizontal axis and is centered on 6.4.

Explanation / Answer

a) z score corresponding to 5% area to its right = 1.645

Hence,

Required hours of sleep = 6.4 + 1.645*1.3 = 8.54 hours

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

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

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