Data Set 8-10: A population with a mean (µ) of 6 and a standard deviation ($\sigma$) of 2. (Carry 3 or 4 decimals in your calculations.)
-See Data Set 8-10. If N = 4, what proportion of the means of a sampling distribution would be less than 3? (Drawing the sampling distribution may help.)
A) .0013
B) .0668
C) .2401
D) .4332
E) .4987

Question

Quizplus · Accepted Answer

The standard error of the mean (SEM) is calculated as $\sigma/\sqrt{N} = 2/\sqrt{4} = 1$. To find the proportion of sample means less than 3, calculate the z-score: $z = (3 - 6)/1 = -3$. Using the standard normal distribution table, the proportion corresponding to a z-score of -3 is approximately 0.0013.

Data Set 8-10: a Population with a Mean (µ) of 6