Final answer:
The question involves calculating the probability of a number of specific outcomes in a binomial distribution, which can be done using either the binomial probability formula or normal approximation for larger datasets.
Step-by-step explanation:
The question is asking about the probability of a certain outcome (the number of cold case victims who knew their murderer) given a particular probability (60% knew their murderer). Since the number of cold cases is 50, this question can be approached using the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n is the number of trials (cold cases), which is 50.
- k is the number of successes (cases where the victim knew their murderer).
- p is the probability of a success on each trial, which is 0.60.
To find the probability for the range of 28 to 33, we would calculate the binomial probability for each value of k within that range and sum them up.
However, with a large number like 50, this could become cumbersome, and it might be more efficient to use normal approximation to the binomial distribution. This would involve finding the z-scores for the lower and upper bounds and then using standard normal distribution tables or a calculator to find the corresponding probabilities.