The Sampling Distribution of a Sample Mean
Sampling Distribution of the Mean
Answers
-
The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled, in this case
. -
The variance of the sampling distribution of the mean is the population variance divided by
. The population SD is
, so the population
variance is
. 
-
The standard error is the standard deviation of the population divided by the square root of
. In this case, 
-
According to the central limit theorem, regardless of the shape of the parent population, the sampling distribution of the mean approaches a normal distribution as
increases. In this case, a sample size of
is
sufficiently large to cause the sampling distribution of the mean to
look about normal. -
Mean =
, SD =
, Skew = about
: This problem is asking about the sampling distribution of the mean: Mean
=
, SD =
=
=
, Skew = about
because the central
limit theorem states that the sampling distribution of the mean would be
about normal with a large enough
.