1. **Problem statement:** Calculate the probability that a student will make a failing score (60% or below) using the cumulative distribution function (CDF). 2. **Formula and explanation:** For a continuous or discrete random variable, the CDF at a value $x$ is $P(X \leq x)$, the probability that the variable takes a value less than or equal to $x$. 3. **Given data:** Scores: 0%, 20%, 40%, 60%, 80%, 100% Probabilities: 0.50, 0.40, 0.30, 0.20, 0.10 (assuming these are probabilities or relative frequencies for each score) 4. **Calculate the probability of failing (60% or below):** This is $P(X \leq 60\%) = P(0\%) + P(20\%) + P(40\%) + P(60\%)$ 5. **Sum the probabilities:** $$P(X \leq 60\%) = 0.50 + 0.40 + 0.30 + 0.20 = 1.40$$ 6. **Interpretation:** Since probabilities cannot exceed 1, the given probabilities likely represent relative frequencies or counts, not probabilities summing to 1. If these are relative frequencies, normalize by dividing each by the total sum. 7. **Normalize probabilities:** Total sum = $0.50 + 0.40 + 0.30 + 0.20 + 0.10 = 1.50$ Normalized $P(X \leq 60\%) = \frac{0.50 + 0.40 + 0.30 + 0.20}{1.50} = \frac{1.40}{1.50} = 0.9333$ **Final answer:** The probability that the student will make a failing score (60% or below) is approximately $0.9333$ or 93.33%.