I'm working on an excercise in which I have problem understanding if I should assume it's discrete or continuous random variable.
The problem states: "Given a population with mean, variance and sample size n equal to $$\mu=100,\ \sigma^2=900,\ n=30$$, what is the probability that $$P(96 <= \bar x <=110)$$
I know how to solve the calculating part and use the Central Limit Theorem, however before that I struggle to understand how I should divide it up depending on the type:
Discrete: $$P(96 <= \bar x <=110) = P(\bar x <= 110) - P(\bar x <= 95)$$
Continuous: $$P(96 <= \bar x <=110) = P(\bar x <= 110) - P(\bar x <= 96)$$
How would I know if it's discrete and therefore use (95) instead of (96)?
Looking at the solution they've used (96) and I assume they think it's continuous.