Assume that 45% of the people in a city agree to implement a new social program ¿Which is the probability that in a sample of 2400 persons less than 1000 of them agree with the program?
First, I decided to model this like $X \sim B(2400,.45)$, then I think we want to find $P(\sum_{i=1}^{2400} X_i<1000)$. Is it possible to model this like a Binomial or does it have to be distributed like a Bernoulli? Is the argument of the probability the one that I need?
Recall that a sum of Bernoulli-distributed random variables is a binomial random variable, so considering the Bernoulli variables $X_i$ independently or the sum of them as binomial, is the same.
On the other hand, since you are adding 2400 (large number in this context) of those variables, using the central limit theorem you may safely approximate your binomial variable as normal variable.
Finally, on the question regarding your probability $P(\sum X_i < 1000)$, yes, this is what you are being asked to calculate.