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

Question

The average time spent sleeping (n hours) for a group of medical residents at a hospital can be appreximated by a normal destibution, as shown in the graph to the right Anewer parts (a) and (b) below leaping Times of Medieal Residents Click to view page 1 of the table lok to iw.page 2 of the table 62 nours (m) What is the shortest tme spert sleegngthat wald stil place a resident inthe tp 5% of sleeping imes? R-te get at least hours of sleep ae nte top 5% of sleeping times Round to two decimal places as needed.) (b) Between what values does the midde 50% of the sleep times lie? The middle 50% of sleep-les between hours on the low end and hours onthe high end. Round to fwo decimal places as needed )

Explanation / Answer

Mean = 6.2 hours

Standard deviation = 1.2 hours

P(X < A) = P(Z < (A - mean) / standard deviation)

a) Let A be the shortest time that would place a member in the top 5%

P(X > A) = 0.05

P(X < A) = 0.95

P(Z < (A - 6.2)/1.2) = 0.95

(A - 6.2)/1.2 = 1.645 (from standard normal distribution table)

A = 8.17

b) Let the middle 50% be between B and C

P(X < B) = 0.25

P(X < C) = 0.75

P(X < (C - 6.2)/1.2 = 0.75

(C - 6.2)/1.2 = 0.67

C = 7.00

(B - 6.2)/1.2 = -6.7

B = 5.40

The middle 50% of sleep times lie between 5.40hours on the low end and 7.00 hours on the high end.

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