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Answer :
To find the probability of a lag time of less than 11 hours, we use the empirical rule, which suggests that approximately 16% of the normal distribution lies more than one standard deviation below the mean when the standard deviation is 2 hours.
The question deals with the concept of the empirical rule, which is a statistical rule stating that for a normal distribution, nearly all data will fall within three standard deviations of the mean.
According to the empirical rule, 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations.
Given that the mean lag time is 13 hours and the standard deviation is 2 hours, we want to find the probability of a lag time of less than 11 hours, which is one standard deviation below the mean.
To apply the empirical rule, we note that approximately 34% of the data lies between the mean and one standard deviation below the mean.
Therefore, we can assume that roughly 34% of the data lies between 11 hours and 13 hours (one standard deviation below and the mean).
Since a normal distribution is symmetrical, about 68% of the data is within one standard deviation of the mean, so this means that 34% of the data lies between 13 hours and 15 hours, and another 34% between 11 hours and 13 hours.
The remaining 16% (half of 32%) lies beyond one standard deviation on both tails of the distribution.
Hence, the probability of a lag time of less than 11 hours is approximately 16%.
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