Final answer:
The probability of various numbers of repeat offenders among 42 randomly selected violent felons can be calculated using the binomial probability formula. The required steps involve summing probabilities for particular ranges, and while tedious by hand, these calculations are more efficiently done using technology.
Step-by-step explanation:
The probability that exactly 25 of the 42 violent felons selected are repeat offenders can be calculated using the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where 'p' is the probability of a felon being a repeat offender, 'n' is the total number of felons selected, and 'k' is the number of repeat offenders. In this case, p = 0.58, n = 42, and k = 25.
To find the probability of at most 24 felons being repeat offenders, we need to sum the probabilities of there being 0 through 24 repeat offenders. A similar approach is used to find the probability of at least 22 felons being repeat offenders, summing probabilities from 22 to 42.
For between 21 and 27 repeat offenders, we sum the probabilities from 21 through 27. These calculations can become cumbersome by hand but are easily handled by technology such as a graphing calculator or statistics software.