According to a comprehensive investigation of blood folate levels in a sample of women aged 16 to 45, this parameter is normally distributed, with a mean of 5.0 ng/mL and a standard deviation of 0.5 ng/mL. According to the findings of the study, 95 percent of serum folate measurements in these individuals will fall roughly between which of the following limits?

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Eductional Objective: A normal (Gaussian) distribution is defined as a symmetrical, bell-shaped distribution curve. One of the most important attributes of the normal distribution is the "68/95/99 rule," which states that 68% of all observations lie within 1 standard deviation (SD) of the mean, 95% within 2 SDs of the mean, and 99.7% within 3 SDs of the mean. The SD is a measure of dispersion or variance (how far the measurements are from one another). In this example, the mean folate level is 5.0 ng/mL with a SD of 0.5 ng/mL. According to the 68/95/99 rule, typically 95 percent of observations fall within 2 standard deviations of the mean, or between 4.0 and 6.0 ng/mL in this situation. These are good estimates; to be more specific, 95 percent of the observations are within 1.96 standard deviations of the mean and 95.45 percent of the observations are within 2 standard deviations of the mean.
It is important to note that SD is used to characterize individual observations in a dataset. Standard error (SE), a similarly related statistic, is used to indicate how closely sample means are linked to population means; SE = SD / n, where n is the sample size.  In this example, if SE had been given instead of SD, investigators would be 95% confident that the true mean folate level in the underlying population lies within the mean +/- 2 SE (which is also the range that would include 95% of sample means calculated from repeated samples of the same size taken from that population).

According to a Comprehensive Investigation of Blood Folate Levels in a Sample