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 Sleeping Times of Medical Residents Click to view page 1 of the table, Click to view page 2 of the table H 6.3 hours ?: 1.3 hour 2 3 4 5 6 7 8 9 10 11 Hours (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 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 betweenU hours on the low end and hours on the high end (Round to two decimal places as needed.) Enter your answer in each of the answer boxes. Save for Later 22 528 20984 JUL

Explanation / Answer

a) From standard normal tables, we get:

P( Z > 1.645 ) = 0.05

Therefore the hours of sleep here is computed as:

= Mean + 1.645* Std Dev = 6.3 + 1.645*1.3 = 8.44

Therefore 8.44 hours is the required answer here.

b) From standard normal tables, we get:

P( -0.6745 < Z < 0.6745 ) = 0.5

Therefore
L = Mean - 0.6745* Std Dev = 6.3 - 0.6745*1.3 = 5.42
?U = Mean + 0.6745* Std Dev = 6.3 + 0.6745*1.3 = 7.18

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