Question

66% of all violent felons in the prison system are repeat offenders. If 35 violent felons are randomly selected, find the probability that

a. Exactly 23 of them are repeat offenders.
b. At most 23 of them are repeat offenders.
c. At least 23 of them are repeat offenders.
d. Between 19 and 25 (including 19 and 25) of them are repeat offenders

Answer 1

To calculate the probabilities of different counts of repeat offenders among 35 violent felons with a 66% repeat offense rate, use the binomial probability formula and sum the appropriate probabilities for each scenario.

Step-by-step explanation:

The question involves calculating probabilities for a binomial distribution since we are dealing with a fixed number of independent trials, two possible outcomes (repeat offender or not), and a constant probability of success (repeat offense).

1. To find the probability of exactly 23 repeat offenders, we use the binomial probability formula P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), where n is the number of trials, k is the number of successes, and p is the probability of success on any given trial.
2. To find the probability of at most 23 repeat offenders, we calculate the sum of probabilities for k = 0 to k = 23.
3. To find the probability of at least 23 repeat offenders, we calculate 1 minus the probability of at most 22 repeat offenders.
4. To find the probability of between 19 and 25 repeat offenders, we calculate the sum of probabilities for k = 19 to k = 25.

Answer 2

The answer is a because if you do 66% of 35 you get 23.1 and that is basically just 23