Final answer:
The probability that at most 2 out of 8 randomly selected businesses have eliminated jobs in the past year, given a 25% job elimination rate, is best calculated using the binomial probability formula. The correct probability is calculated to be 0.2656.
Step-by-step explanation:
The question asks to find the probability that at most 2 of 8 randomly selected businesses have eliminated jobs in the past year when it is known that 25% of businesses have eliminated jobs. This is a binomial probability problem because there are only two possible outcomes for each business (either they have eliminated jobs or they have not), a fixed number of trials (8 businesses), and the probability of success (a business having eliminated jobs) is 0.25 for each trial.
To solve this, we will use the binomial probability formula:
P(X ≤ k) = Σ₀ⁿ¹¹[⁹Cₓ × (0.25)^ₓ × (0.75)^⁹ₓ]
Where P(X ≤ k) is the probability of at most k successes, ⁹Cₓ is the combination of 9 trials taken r at a time, (0.25) is the probability of success, and (0.75) is the probability of failure.
The probability for 0, 1, and 2 job eliminations can be calculated and summed up to find the probability for at most 2 eliminations: P(X=0) + P(X=1) + P(X=2).
After calculating, we find that the probability is 0.2656, which matches option a.