EXAMPLE 5.4

Total sleep time of college students. A recent survey describes the distribution of total sleep time among college students as approximately Normal with a mean of 6.78 hours and standard deviation of 1.24 hours.³ Suppose that we select a college student at random and obtain his or her sleep time. This result is a random variable X because, prior to the random sampling, we don’t know the sleep time. We do know, however, that in repeated sampling, X will have the same N(6.78, 1.24) distribution that describes the pattern of sleep time in the entire population. We call N(6.78, 1.24) the population distribution.