Question

Without using a normal curve table, about what percentage of scores on a normal curve are (a) between the mean and 2 SDs above the mean (b) below 1 SD above the mean (c) above 2 SDs below the mean?

a) (a) 47.5%, (b) 34%, (c) 2.5%
b) (a) 34%, (b) 13.5%, (c) 2.5%
c) (a) 68%, (b) 34%, (c) 13.5%
d) (a) 50%, (b) 16%, (c) 84%

Answer 1

The Empirical Rule in statistics indicates that approximately 47.5% of scores lie between the mean and 2 SDs above the mean, about 34% of scores are below 1 SD above the mean, and around 2.5% of scores are above 2 SDs below the mean.

Step-by-step explanation:

The question pertains to the application of the Empirical Rule in statistics, which is used to determine the percentage of data falling within certain intervals of the standard deviation in a normal distribution.

1. (a) Between the mean and 2 SDs above the mean, about 47.5% of scores lie.
2. (b) Below 1 SD above the mean, about 34% of scores lie.
3. (c) Above 2 SDs below the mean, about 2.5% of scores lie.

The correct answer to the student's question would therefore be (a) 47.5%, (b) 34%, (c) 2.5%, which matches option 'a' from the given choices.