Question

Mathieu grows specialty tomatoes that are much larger than typical tomatoes. The distribution of their weights is strongly skewed to the left with a mean of 232g and a standard deviation of 12g. Suppose we were to calculate the mean weight from a random sample of 16 of Mathieu's tomatoes. We can assume independence between tomatoes in the sample.

What is the probability that the mean weight from the sample of 16 tomatoes x is within 6g of the population mean?

Answer 1

We cannot calculate this probability because the sampling distribution is not normal.

Explanation:

Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.