# How to calculate the likelyhood that a single measurement "belongs" to a standard distribution?

(Apologies in advance for using wrong terms and probably asking the wrong question)

Given a standard distribution with some $$\mu$$ and $$\sigma$$, and a single measurement $$m$$. Can I calculate the likelihood that $$m$$ "belongs" to the given standard distribution?

For context: I'm working on a real-time monitoring solution. We measure a count at a regular interval. The measured counts follow a normal distribution, which give me my $$\mu$$ and $$\sigma$$. Now given an alerting threshold, I want to calculate the specificity (for false positives) and sensitivity (for false negatives). Calculating the specificity is straightforward using the CDF. I'm struggling with calculating the sensitivity though. If I can calculate the likelihood that a measurement "belongs" to the normal distribution, then I can calculate the sensitivity. But I don't know how to do this, hence this question.

You just want to calculate how many standard deviations ($$\sigma$$) your observation ($$m$$) is away from the mean ($$\mu$$) and then apply z-score relations to find the probability of the observation.