Question

What percentage of the sample means are within two standard deviations above or below the mean?

a. 95%
b. 68%
c. 99.7%
d. 50%

Answer 1

Approximately 95% of the sample means lie within two standard deviations of the mean, according to the Empirical Rule for normal distributions.

Step-by-step explanation:

The question you've asked pertains to the Empirical Rule in statistics, which is a statement about normal distributions. According to this rule, for a data set that has a bell-shaped and symmetric distribution, approximately 95% of the sample means lie within two standard deviations of the mean. So, the answer to your question is a. 95%.

To find the value that is two standard deviations above the expected value (mean) of a sample mean, you would use the formula:

• Expected value + (2 × Standard Deviation)

Assuming an expected value (mean) of 90 and a known standard deviation, you would simply plug in these numbers to get the specific value.