Sampling distribution of the sample minimum

Hi! I’m taking de Data Science path and I have a doubt about sampling distributions. I got stuck in this question: " * Use the sampling distribution of the sample minimum to estimate the probability of observing a specific sample minimum. For example, from the plot, what is the chance of getting a sample minimum that is less than 130bpm?" ( )
I don’t understand if I have to use the CDF to calculate the propability in this way stats.norm.cdf(130, population_min, standard_error) or it is wrong, because the answer is 100% of probability. Please, I need to understad when to use CDF or with what statistics is right to use.

Thank you!

It’s all in the name right (but also the formula haha).

Cumulative Density Function represents the probability that the random variable X takes on a value less than or equal to (little) x. Note that it is not the same as it being the probability of it taking the value x.

For getting the values of a specific interval, or a single value (depending on whether it’s continuous or discrete) you might want to look into the PDF and PMF, respectively.

I’ll say with the continuous ones it’s good at least having a high-level understanding of what the calculus is doing to have a clear picture of what the different functions aim to do. No need to do double or triple integrals by hand, but it’s at least useful to know why they’re used.


I really like this resource for fundamentals of statistics:

I have the hard-copy of the book and the youtube lectures are great too.


Thank you! I’ll read it.

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