A large study of serum folate levels in a sample of women age 16-45 reveals that 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 study results, 95% of serum folate observations in these patients will lie approximately between which of the following limits?

Question

A large study of serum folate levels in a sample of women age 16-45 reveals that 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 study results, 95% of serum folate observations in these patients will lie approximately between which of the following limits?

Quizplus · Accepted Answer

11ec160b_3707_9d99_9249_8770a1829cdd_MD0001_00 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. Therefore: Based on the 68/95/99 rule, approximately 95% of observations lie within 2 SDs of the mean, so between 4.0 and 6.0 ng/mL in this case. These are helpful approximations; to be more precise, 95% of the observations lie within 1.96 SDs of the mean and 95.45% of the observations lie within 2 SDs of the mean. Note that SD is used to describe individual observations in a dataset. A closely related measure called standard error (SE) is used to show how closely sample means are related 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). (Choices A and D) These limits are asymmetric and are therefore inconsistent with a normal distribution curve around the mean. (Choice B) Approximately 99.7% of all observations lie within 3 SDs of the mean (3.5-6.5 ng/mL). (Choice E) Approximately 68% of all observations lie within 1 SD of the mean (4.5-5.5 ng/mL). Educational objective: In a normal (bell-shaped) distribution curve, 68% of observations lie within 1 standard deviation (SD) of the mean, 95% of observations lie within 2 SDs of the mean, and 99.7% of observations lie within 3 SDs of the mean.

A Large Study of Serum Folate Levels in a Sample