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Difficulty: HardMulti-Statement Boolean Evaluation

The table below details operational telemetry for eight municipal battery energy storage system (BESS) microgrid zones during 2025:

Zone CodeBattery Capacity (MWh)Annual Energy Discharged (GWh)Peak Efficiency (%)Unplanned Maintenance (Hours)
Zone Alpha12043.292.548
Zone Beta20084.095.012
Zone Gamma15051.089.072
Zone Delta300117.094.224
Zone Epsilon8026.491.096
Zone Zeta250105.096.518
Zone Eta18059.488.560
Zone Theta22085.893.036

Consider the following three independent statements:

I. If the zones are sorted in ascending order by Battery Capacity (MWh), the median Peak Efficiency (%) of the lower half of the sorted zones is greater than 90.5%90.5\%.
II. The average annual energy discharged per MWh of battery capacity across the three zones with the fewest unplanned maintenance hours is strictly greater than 0.40 GWh per MWh0.40\text{ GWh per MWh}.
III. Among the zones with a Peak Efficiency of at least 92.0%92.0\%, exactly four zones recorded fewer than 4040 unplanned maintenance hours.

Based on the table provided, is the evaluation that Statement I is False, Statement II is True, and Statement III is True correct?

Answer: Answer

Answer

The overall evaluation is True because Statement I is False, Statement II is True, and Statement III is True.
Evaluating all three statements shows that Statement I is False (90.0%≯90.5%90.0\% \ngtr 90.5\%), Statement II is True (0.408>0.400.408 > 0.40), and Statement III is True (44 zones meet both criteria). Thus, the proposed outcome (False, True, True) accurately describes the dataset.

Step-by-Step Solution

1
Evaluate Statement I by sorting zones by Battery Capacity and finding the median Peak Efficiency of the lower half.
Sorted capacity order: Epsilon (8080), Alpha (120120), Gamma (150150), Eta (180180), Beta (200200), Theta (220220), Zeta (250250), Delta (300300). Lower half: Epsilon (91.0%91.0\%), Alpha (92.5%92.5\%), Gamma (89.0%89.0\%), Eta (88.5%88.5\%). Efficiencies sorted: 88.5%88.5\%, 89.0%89.0\%, 91.0%91.0\%, 92.5%92.5\%. Median = 89.0%+91.0%2=90.0%\frac{89.0\% + 91.0\%}{2} = 90.0\%. Since 90.0%≤90.5%90.0\% \le 90.5\%, Statement I is False.
Determines whether Statement I is correctly classified as False.
2
Evaluate Statement II by identifying the three zones with the minimum unplanned maintenance hours and computing their aggregate discharge per MWh of capacity.
Fewest maintenance hours: Zone Beta (12 hrs12\text{ hrs}), Zone Zeta (18 hrs18\text{ hrs}), Zone Delta (24 hrs24\text{ hrs}). Sum of energy discharged = 84.0+105.0+117.0=306.0 GWh84.0 + 105.0 + 117.0 = 306.0\text{ GWh}. Sum of capacity = 200+250+300=750 MWh200 + 250 + 300 = 750\text{ MWh}. Rate = 306.0750=0.408 GWh/MWh\frac{306.0}{750} = 0.408\text{ GWh/MWh}. Since 0.408>0.400.408 > 0.40, Statement II is True.
Determines whether Statement II is correctly classified as True.
3
Evaluate Statement III by filtering zones with Peak Efficiency ≥92.0%\ge 92.0\% and counting how many have unplanned maintenance hours under 4040.
Zones with Peak Efficiency ≥92.0%\ge 92.0\%: Alpha (92.5%92.5\%, 48 hrs48\text{ hrs}), Beta (95.0%95.0\%, 12 hrs12\text{ hrs}), Delta (94.2%94.2\%, 24 hrs24\text{ hrs}), Zeta (96.5%96.5\%, 18 hrs18\text{ hrs}), Theta (93.0%93.0\%, 36 hrs36\text{ hrs}). Those with maintenance hours <40< 40: Beta, Delta, Zeta, Theta (44 zones). Statement III is True.
Determines whether Statement III is correctly classified as True.

Key Concept

Multi-Statement Boolean Evaluation in Tabular Data
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Topics

Multi-Statement Boolean Evaluation

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