example: Describe the sampling distribution of for samples of size 15 drawn from a normal
population with mean 65 and standard deviation 9.
solution: Because the original population is normal, is normal with mean 65 and standard
deviation . That is, has .example: Describe the sampling distribution of for samples of size 15 drawn from a population
that is strongly skewed to the left (like the scores on a very easy test) with mean 65 and
standard deviation 9.
solution: μ = 65 and σ = 2.32 as in the above example. However this time the population is
skewed to the left. The sample size is reasonably large, but not large enough to argue, based on
our rule of thumb (n ≥ 30), that the sampling distribution is normal. The best we can say is that
the sampling distribution is probably more mound shaped than the original but might still be
somewhat skewed to the left.example: The average adult has completed an average of 11.25 years of education with a standard
deviation of 1.75 years. A random sample of 90 adults is obtained. What is the probability that
the sample will have a mean
(a) greater than 11.5 years?
(b) between 11 and 11.5 years?
solution: The sampling distribution of has μ = 11.25 and