A local steakhouse served 625 customers over a weekend. The distribution of each customer's food purchase is non-normal. The average cost of each customer's food purchase is 52 dollars, with a standard deviation of 17 dollars. Suppose that a random sample of 315 customers are selected from the weekend's customers. Would it be appropriate to model the distribution of the sample mean with a normal model? No. The mean distribution theorem states that the sampling distribution of the sample mean can only be modeled by the non-normal model because the population distribution is non-normal.
There is not enough information to make assumptions regarding the distribution of the sample mean.
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.
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.
Yes. The mean distribution 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 population distribution.