Question

The average time spent sleeping (in hours) for a group of medical residents at a hospital can be approximated by a normal distribution, with mean of 6.1 hours and standard deviation of 1.0 hour. Let x represents a random medical resedent selected at the hospital. Find P(x < 5.3).

Answer 1

First we calculate the z-score for this situation.
$Z=\frac{X- \mu}{\sigma} = \frac{5.3-6.1}{1} = -0.8$
Finding P(x < 5.3) is the same as finding P(z < -0.8).  Using a table of standard normal distribution and z-scores we see that the probability is 0.21186.