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

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... 1 2 3 4 5 6 7 8 9 10 Bold Sleeping Times of Sleeping Times of Bold Medical Residents Medical Residents mu equals 5.7 hours =5.7 hours sigma equals 1.2 hour =1.2 hour Hours Hours 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 = 5.7 hours and sigma = 1.2 hour is over the horizontal axis and is centered on 5.7. (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. (Round to two decimal places as needed.)

Explanation / Answer

Result:

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... 1 2 3 4 5 6 7 8 9 10 Bold Sleeping Times of Sleeping Times of Bold Medical Residents Medical Residents mu equals 5.7 hours =5.7 hours sigma equals 1.2 hour =1.2 hour Hours Hours 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 = 5.7 hours and sigma = 1.2 hour is over the horizontal axis and is centered on 5.7.

z value for top 5% = 1.645 ( from standard normal distribution)

x= +z*

x = 5.7+1.645*1.2 =7.674

=7.67 ( two decimals)

(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.)

Z values for middle 50% = (-0.674, 0.674)

Lower value = 5.7-0.674*1.2 =4.8912

upper value = 5.7+0.674*1.2 =6.5088

The values are (4.89, 6.51)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.