Step 1 :The problem is asking us to compare the probabilities of different events in a normally distributed population. The events are the probabilities that the sample mean falls within a certain range, for different sample sizes, and the probability that a single observation falls within that range.
Step 2 :The key to solving this problem is understanding the concept of the standard error of the mean. The standard error of the mean is a measure of the dispersion of the sample mean around the population mean. It is equal to the standard deviation divided by the square root of the sample size.
Step 3 :As the sample size increases, the standard error decreases, meaning that the sample mean is more likely to be close to the population mean.
Step 4 :Therefore, for a larger sample size, the probability that the sample mean falls within a certain range around the population mean is higher.
Step 5 :So, the order from least to greatest should be (c), (b), (a).
Step 6 :\(\boxed{\text{The order from least to greatest is (c), (b), (a).}}\)