The inverse cumulative distribution function (CDF) for a binomial distribution with p=0.05 and n=30 at probability 25% means we need to find the smallest number of successes k such that P(X ≤ k) ≥ 0.25.

Calculating:

• P(X=0) = (0.95)^30 ≈ 0.2146
• P(X=1) = C(30,1) * (0.05)^1 * (0.95)^29 ≈ 30 * 0.05 * 0.2260 ≈ 0.339

Cumulative probabilities:

• P(X ≤ 0) = 0.2146 < 0.25
• P(X ≤ 1) = 0.2146 + 0.339 = 0.5536 ≥ 0.25

Therefore, the smallest k where P(X ≤ k) ≥ 0.25 is k=1, so the answer is One success.