Final answer:
The correct option is not listed .To find the probability that exactly sixty-eight out of seventy randomly selected students feel that courts show too much concern for criminals, the binomial probability formula should be used. However, after performing the calculation, none of the provided answer choices match the result, suggesting an error in the question or options presented.
Step-by-step explanation:
The student has posed a question regarding the probability of a specific survey outcome. The survey suggests that three out of four students believe that courts show too much concern for criminals. The probability question asks us to calculate the likelihood that exactly sixty-eight out of seventy randomly selected students will share this opinion.
To solve the problem, we can use the binomial probability formula, since each student's response (showing too much concern or not) can be considered a Bernoulli trial with two possible outcomes. The formula is given by:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of k students showing concern,
- C(n, k) is the combination of n students taken k at a time,
- p is the probability of a single student showing concern,
- n is the total number of students (70),
- k is the desired number of students (68).
Given that 3/4 (= 0.75) students show the concern, the probability (p) is 0.75:
P(X = 68) = C(70, 68) * (0.75)^68 * (0.25)^2
After calculating this value, we find that none of the provided options (A, B, C, D, E) match the computed probability, which means the correct option is not listed or there is a problem with the question as it is currently stated.