i. For a normal probability distribution, about 95 percent of the area under normal curve is within plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area under the normal curve is within three standard deviations of the mean. ii. The total area under the normal curve is 100%.
iii. The mean of a normal probability distribution is 500 and the standard deviation is 10.
About 95 percent of the observations lie between 480 and 520.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

Statement (i) is correct as it describes the empirical rule for normal distributions. Statement (iii) is correct because 480 and 520 are two standard deviations away from the mean of 500 (mean ± 2*10). Statement (ii) is incorrect because the total area under the normal curve is 1 (or 100%), not 100% as a separate value.

I for a Normal Probability Distribution, About 95 Percent of the Area