A 1000-acre farm historically averages 193 bushels per acre with a standard deviation of 16 bushels per acre.Fifty acres are sampled and the mean yield determined.If we imagined all the possible random samples of 50 acres we could take and looked at all the sample means,is it appropriate to assume this data will be well modeled by a Normal distribution?
A)The Normal distribution can be used since the original population has a Normal distribution.
B)The Normal distribution cannot be used.The distribution in the sample should resemble that in the population,which may be skewed by some acres with extremely low yields.
C)The Normal distribution can be used since the samples can be assumed to be random and independent.However,there could be some doubt since weather conditions could affect all samples.The sample size,50,is no more than 10% of the population of all acres on the farm.
D)The Normal distribution cannot be used since the sample size is not large enough for the Central Limit Theorem to apply.
E)The Normal distribution can be used since the sample size,50,is no more than 10% of the population of all acres on the farm.

Question

Quizplus · Accepted Answer

The sample size is large enough for the Central Limit Theorem to apply, but there may be doubt since weather conditions could affect all samples. However, the samples can be assumed to be random and independent.

A 1000-Acre Farm Historically Averages 193 Bushels Per Acre with a Standard