Select the correct answer.
Over the past month, a garment manufacturer produced 800 dresses. The distribution of the amount of fabric required to make the dresses is not normal.
The average amount of fabric needed to make a dress is 4 yards, with a standard deviation of
of a yard. Suppose a series of samples, each containing 180 dresses, are selected from the dresses produced in the past month.
Would it be appropriate to model the distribution of a sample mean with a normal model?
A.
No. The central limit theorem states that the sampling distribution of a sample mean can only be modeled by a non-normal model because the population distribution is non-normal.
B.
There is not enough information to make assumptions regarding the distribution of the sample mean.
C.
No. The central limit theorem states that the sampling distribution of a sample mean can only be modeled by a normal model if the sample size is large enough and the shape of the population distribution is normal.
D.
Yes. The central limit theorem states that the sampling distribution of a sample mean can be modeled by a normal model if the sample size is large enough, regardless of the shape of the population distribution.