A population has a standard deviation of 16.If a sample of size 64 is selected from this population,what is the probability that the sample mean will be within
2 of the population mean?
A)0.6826
B)0.3413
C)-0.6826
D)Since the mean is not given,there is no answer to this question.

Question

A population has a standard deviation of 16.If a sample of size 64 is selected from this population,what is the probability that the sample mean will be within 
2 of the population mean?
A)0.6826 
B)0.3413 
C)-0.6826 
D)Since the mean is not given,there is no answer to this question.

Quizplus · Accepted Answer

Since the population standard deviation is known and the sample size is large enough (n=64), we can use the central limit theorem to approximate the distribution of sample means as normal.  The formula for the standard error of the mean is:

standard error = population standard deviation / square root of sample size

= 16 / sqrt(64)

= 2

Therefore, the probability of the sample mean being within 2 standard errors (2 x 2 = 4) of the population mean is approximately 0.6826 or 68.26%. This can be found using a standard normal distribution table or calculator.

A Population Has a Standard Deviation of 16