Suppose the weights of apples in an orchard are normally distributed with a mean of $150$ grams and a standard deviation of $30$ grams. What effect does increasing the sample size have on the probability that the sample mean weight is close to $150$ grams? Explain your reasoning.

• A. It increases the probability that the sample mean is close to $150$ grams
• B. It has no effect on the probability that the sample mean is close to $150$ grams
• C. It decreases the probability that the sample mean is close to $150$ grams
• D. It decreases the standard deviation of the population, making the sample mean closer to $150$ grams

Answer: (A)