the mean annual income for adult women in one city is and the standard deviation of the incomes is The distribution of incomes is skewed to the right. For samples of size 30, which of the following statements best describes the sampling distribution of the mean?
To determine the best description of the sampling distribution of the mean, we need to consider the characteristics of the population distribution, sample size, and the central limit theorem.
The central limit theorem states that, regardless of the shape of the population distribution, the sampling distribution of the mean approaches a normal distribution as the sample size increases.
Given that the population distribution of incomes is skewed to the right, the sampling distribution of the mean for samples of size 30 will be approximately normal. This is because the sample size is relatively large, allowing the central limit theorem to take effect and overcome the skewness of the population distribution.
Therefore, the best statement describing the sampling distribution of the mean would be: The sampling distribution of the mean will be approximately normally distributed.