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Ventilation Design Handbook on Animal Research Facilities Using Static Microisolators 
The odds of obtaining a score within -1.96 and +1.96 are 95 out of 100, therefore, the odds of a 
score being outside that range are five in 100. The latter situation has a probability of less than 
0.05, and would use p-value<0.05, to indicate the probability of occurrence. Events which occur 
only 5 times out of 100 are rare events. These rare events can be considered significant because 
of their infrequent occurrence. 
6.1.5 Standard Error of the Mean 
Much of statistics pertains to inferential statistics where we infer population values from sample 
values. In a typical situation, a sample might be taken and the mean and standard deviation 
computed. From these data, one will want to infer that the population values are identical or at 
least similar. In other words, it is hoped that the sample data reflects the population data. 
Considering a situation in which many samples are taken to determine a mean and standard 
deviation for each sample, the obtained z-score mean values would be distributed in the same 
normal distribution as the raw z-scores. Consider the illustration below. Conceptualize a large 
population where the mean score on a test is 35. Samples drawn from the population would yield 
different sample means. 
The same normal curve graph can be applied to the z-score means that was applied to the 
individual scores. For example, 95 percent of the z-score means would fall within the range of 
-1.96 to +1.96. 
