Among Canadian households, 24% have telephone answering machines. If a telemarketing company contacts 2500 households find the probability that between 625 and 650 households, inclusive, have answering machines.

never mind i got it lol

To find the probability that between 625 and 650 households, inclusive, have answering machines, we need to use the Binomial Probability Formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:
- P(X = k) is the probability of getting exactly k successes
- n is the number of trials (number of households contacted)
- k is the number of successes (number of households with answering machines)
- p is the probability of success in one trial (probability of a household having an answering machine)
- C(n, k) is the number of combinations of n objects taken k at a time (number of ways to choose k households out of n)

Here's how we can apply this formula to solve the problem:

1. Calculate the number of trials (n) which is 2500.
2. Calculate the probability of success (p) which is 24% or 0.24.
3. Calculate the number of successes within the desired range (between 625 and 650, inclusive).

To find the probability that between 625 and 650 households have answering machines, we need to sum up the probabilities of each individual number of successes within that range.

P(625 ≤ X ≤ 650) = P(X = 625) + P(X = 626) + ... + P(X = 650)

Calculate each individual probability using the binomial formula:

P(X = k) = C(2500, k) * 0.24^k * (1 - 0.24)^(2500 - k)

Sum up all the individual probabilities for k ranging from 625 to 650 to get the final answer.