Probability of a sample

Question: If the standard deviation of a population is known can one calculate the probability of sample with a given standard deviation calculated from the sample?


Ambassador to the humans
Are you assuming the population is normally distributed? Or do you at least have some sort of assumption about the distribution of the population?

And by "calculate the probability of sample with a given standard deviation" I assume you don't mean just "what is the probability the sample will have a standard deviation of EXACTLY 3" but instead something like "what is the probability the sample standard will be greater than or equal to 3"?
Hi Dason, Thanks for your reply. Good questions. It's about a normal distribution. And we need to fix sample size. Say the standard deviation (SD) of the population is 8.1, is finding the probability of a sample with a calculated sample SD of 5 a legitimate question? Or we could only find the chance of all samples with SD <5 ? Gary


Ambassador to the humans
Since the sample SD is a continuous random variable the probability of getting exactly 5 if always 0 regardless of the parameters.

Just to help think about that imagine the sample SD is 6 would you classify that as being equal to 5? What about 5.5? 5.0000001?

We can calculate probabilities for ranges/intervals but the probability it will exactly equal some value is always 0.

Providing info on why you want to do this might help us help you figure out the appropriate question for what you want.