A sampling distribution has a mean of 100 and a standard error of 2. What percent of samples will get sample results between 98 and 102?
A) 2%
B) 4%
C) 68%
D) 95%

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the means will be normally distributed with a mean of 100 and a standard error of 2. Therefore, we can calculate the z-scores for the values of 98 and 102 as follows:

z(98) = (98 - 100) / 2 = -1
z(102) = (102 - 100) / 2 = 1

Then, we can use a z-table or a calculator to find the proportion of samples with z-scores between -1 and 1. This area represents the percentage of samples with sample means between 98 and 102.

Using a z-table, we can find that the area under the standard normal curve between -1 and 1 is approximately 0.6827, or 68.27%. Therefore, about 68% of samples will get sample results between 98 and 102. Thus, the answer is C.

A Sampling Distribution Has a Mean of 100 and a Standard