Question

Assume a specific sample size. This would be the number of individuals in the group. Using that sample size, determine the range within which the group's average iron level would be consider usual. Describe how you arrived at that range using the Central Limit Theorem and the Empirical Rule.

Answer 1

Central Limit Theorem : For large sample size ( n ) the sampling distribution of sample mean follows

approximate normal distribution.

For normal distribution about 95% lies between -1.96 * and 1.96 * . Where is the standard

error of the sample mean.

Therefore the range within which the group's average iron level would be consider usual is

from -1.96 * to 1.96 * .

Empirical Rule : About 95% data lies between 2 times standard deviation.

Therefore the range within which the group's average iron level would be consider usual is

from -2* to 2* .