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Jump Qualification A401C2

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1. State the problem: To qualify for the 2nd round students need to jump at least 1.3 m. How many students qualified for the 2nd round? 2. Formula and important rules: To count qualified students we count those with jump height $h$ satisfying $h \ge 1.3$. If you have individual heights $h_1, h_2, \dots, h_n$ the count is given by the indicator sum $$N = \sum_{i=1}^n \mathbf{1}(h_i \ge 1.3)$$ Students who jumped exactly 1.3 m qualify because the inequality is $\ge$. 3. How to proceed with the available data: If you have a list of heights, evaluate the indicator for each and sum. If you have a frequency table of exact heights, sum frequencies for heights $\ge 1.3$. If you have grouped data, add full bin frequencies for bins entirely above 1.3 and add a proportion of the bin that crosses 1.3 if needed. 4. Worked example with a small hypothetical dataset: Suppose heights in metres are $[1.05, 1.40, 1.30, 1.29, 1.60]$. Compute indicators: $\mathbf{1}(1.05 \ge 1.3) = 0$ $\mathbf{1}(1.40 \ge 1.3) = 1$ $\mathbf{1}(1.30 \ge 1.3) = 1$ $\mathbf{1}(1.29 \ge 1.3) = 0$ $\mathbf{1}(1.60 \ge 1.3) = 1$ Summing gives $$N = 0 + 1 + 1 + 0 + 1 = 3$$ So in this example 3 students qualified. 5. Final answer and what I need from you: With the information you gave I cannot determine the actual number because the students' jump heights or a frequency table were not provided. Please provide the list of jump heights or a table of frequencies and I will compute the exact number qualified using the steps above.