Which of the following is true regarding the standard deviation?
A) It indicates the degree of variation in the values in such a way as to be translatable into a normal curve.
B) One standard deviation above and below the midpoint in a normal distribution includes 68 percent of the area underneath the curve.
C) + or - 1.96 standard deviations above and below the midpoint in a normal distribution includes 95 percent of the area underneath the curve.
D) + or - 2.58 standard deviations above and below the midpoint in a normal distribution includes 99 percent of the area underneath the curve.
E) All of the above are correct.

Question

Quizplus · Accepted Answer

All of the statements are true regarding the standard deviation. The standard deviation is a measure of the spread of a distribution, and it can be used to calculate the probabilities of different outcomes in a normal distribution. In particular, choice B is referring to the empirical rule, which states that about 68% of the observations in a normal distribution are within one standard deviation of the mean, while choice C and D are referring to the 95% and 99% confidence intervals for a normal distribution, respectively.

Which of the Following Is True Regarding the Standard Deviation