Farmer Joe the statistical farmer has a large corn field and has been told the average
number of corn kernels on an ear of corn is 800 with a standard deviation of 34 kernels and
that the distributions of kernels per ear is unimodal, symmetric, and triangular in shape.
a) Suppose Joe plans on selecting 20 ears of corn and computing the mean number of
kernels per ear for this sample. Can we still say the distribution of sample means will
be approximately normal even though the sample size is less than 30? Explain.
b) If Joe selects a simple random sample containing 20 ears of corn, what is the
probability he will end up with less than 15700 kernels of corn?
(If the number of kernels is less than 15700, what does this mean about the mean
number of kernels per ear of corn?)