A standardized test is known to be Normally distributed with the mean of 500 and the standard deviation of 100. How large a sample would be needed if the standard deviation of sample means is 14?
A) 30
B) 42
C) 51
D) 82

Question

Quizplus · Accepted Answer

The standard error (SE) of the mean is calculated as: SE = SD/sqrt(n). 
Since the population standard deviation is known (SD = 100), we can rearrange the formula as: n = (SD/SE)^2. 
Substituting SD=100 and SE=14, we get n = (100/14)^2 = approximately 51. Therefore, the sample size required is 51. So, the correct answer is C.

A Standardized Test Is Known to Be Normally Distributed with the Mean