What is the probability of getting a sample mean between 500 and 520 if the population mean is 500 and the standard deviation of the sampling distribution (the standard error of the mean)is 20?
A)0.5000
B)0.4332
C)0.3413
D)0.1915

Question

Quizplus · Accepted Answer

First, we need to find the z-scores for both the upper and lower limits:

Lower limit: (500-500)/20 = 0 
Upper limit: (520-500)/20 = 1

Using a z-table, we can find the probabilities associated with these z-scores:

Lower limit: 0.5000 
Upper limit: 0.8413

To find the probability of the sample mean falling between these two limits, we subtract the lower probability from the upper probability:

0.8413 - 0.5000 = 0.3413

Therefore, the answer is C.

What Is the Probability of Getting a Sample Mean Between