Final answer:
The probability that exactly sixty-eight out of seventy students feel that courts show too much concern for criminals is extremely low, almost 0, due to the significant deviation from the expected number of students who would have this opinion.
Step-by-step explanation:
We are asked to find the probability that out of seventy randomly selected students exactly sixty-eight feel that courts show too much concern for criminals, given that three out of four students, or 75%, have this opinion.
This question can be solved using the binomial probability formula:
P(X=k) = nCr * p^k * (1-p)^(n-k)
Where n is the number of trials, k is the number of successes, p is the probability of success on a single trial, and nCr is the combination of n items taken k at a time.
Therefore, the probability that exactly sixty-eight out of seventy students feel that courts show too much concern for criminals is:
P(X=68) = 70C68 * (0.75)^68 * (0.25)^2
Given the high values for n and k, this calculation will yield a very low probability, suggesting that the probability is not 1 (option A), and without doing a precise calculation, based on the binomial distribution properties and the high deviation from the expected number of successes (which would be 70*0.75=52.5), it is going to be very close to 0, which corresponds to option B (0.8265) or option C (0).