The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution. The average is 6.1 hours with a standard deviation of 1 hour. a. What is the shortest time spent sleeping that would place a resident in the top 5% of sleeping times

7.75 hours

Step-by-step explanation:

Given that:

Mean, m = 6.1

Standard deviation, s = 1

Shortest Time spent sleeping in other to be in top 5% of sleeping time.

5% = 0.05

Zscore for P(Z > 0.05) = 1.645 (Z probability calculator)

To obtain the shortest time, x

Zscore = (x - m) / s

1.645 = (x - 6.1) / 1

1.645 = x - 6.1

1.645 + 6.1 = x

7.745 = x

x = 7.75

Sgirtws sleep time = 7.75 hours

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step-by-step explanation: