Final answer:
In a right-skewed distribution with an average income of $62,000 and standard deviation of $27,000, a random sample of 100 residents is large enough for the Central Limit Theorem to apply because the sample size exceeds the general threshold of 30 for the CLT. This allows the sample mean to be considered approximately normally distributed.
Step-by-step explanation:
The question pertains to whether a sample size is large enough to use the Central Limit Theorem (CLT) for means in a distribution with a known average income and standard deviation that is right-skewed. The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution.
In the specific scenario given, the average income in the region in 2013 was $62,000 per person per year with a standard deviation of $27,000, and we are considering a random sample of 100 residents. According to the CLT, the sample size is considered large enough if it is 30 or more, as a general rule of thumb. Therefore, with a sample size of 100, which is greater than 30, the sample size is indeed large enough to apply the Central Limit Theorem. This allows us to make inferences about the population mean from the sample mean, such as calculating confidence intervals or performing hypothesis tests, under the assumption that the sample mean will follow a normal distribution.