From Point Estimates to Population Risk: A Stochastic Analysis of Time Demand and Supply in a 16-Credit Accelerated Nursing Program

1. Introduction

Educational workload analysis fundamentally compares two quantities: the time demanded by academic requirements versus the time available to students after accounting for physiological necessities. Our previous deterministic analysis of a 16-credit summer nursing program established a clear mathematical impossibility (Moslow, 2025):

This calculation, while mathematically sound, embodies a critical limitation: it assumes every student requires identical time to complete each task. Decades of educational research document substantial variation in student processing speeds, with medical reading rates ranging from below 100 WPM to over 200 WPM (Klatt & Klatt, 2011), representing a 2-3× performance range within the same cohort.

Multiple empirical studies establish that student populations exhibit predictable performance variations. Medical students demonstrate reading speeds for clinical content ranging from 50-100 WPM, compared to 250-300 WPM for general texts. Critically, 66% of medical students read below 100 WPM for medical content, while 17% read below 150 WPM even after extensive practice (Klatt & Klatt, 2011). This creates a fundamental disparity where slower readers require 2-3× longer for identical assignments. English as Additional Language (EAL) students show persistent reading speed gaps of approximately 30 WPM compared to native speakers, even after a full academic year (Schmidtke, Rahmanian, & Moro, 2024). For nursing texts with high technical density, this translates to approximately 1.5× longer reading times (Huang et al., 2020). While students can watch educational videos at 1.5-2× speed with minimal comprehension loss (Chen, Kumar, Varkhedi, & Murphy, 2024), actual behavior varies. Deep processors frequently pause and rewatch segments, extending viewing time to 1.5× runtime, while efficient learners utilize speed controls to complete videos in 0.9× runtime (Murphy et al., 2022). Commute times correlate negatively with academic performance, with students traveling >60 minutes showing significantly lower GPAs (Guan et al., 2025). Urban nursing students report commute times ranging from 30-90 minutes each way, creating a 15-45 hour weekly variation in time availability.

This study applies stochastic modeling to capture population heterogeneity in nursing student workload. We aim to replace point estimates with probability distributions for all academic tasks, model distinct student archetypes based on empirical performance data, quantify the full distribution of workload experiences via Monte Carlo simulation, identify the proportion of students facing physiologically unsustainable demands, and propose evidence-based interventions targeting the most vulnerable students.

2. Methods

2.1 Base Data from Deterministic Analysis

We retained all 194 discrete tasks catalogued from the official course syllabi, preserving task categories, durations, and weekly distributions. Note: The original deterministic analysis erroneously reported 558 tasks due to methodological overcounting (likely counting individual pages, clinical hours, or subtasks separately). Verification against actual syllabi reveals 194 distinct assignments across four courses. Table 1 summarizes the base time allocations that serve as means (μ) for our probability distributions.

*Examination time is distributed within the class time allocation to avoid double-counting. **Video content includes substantial Module 5 extended content (4.3 additional hours) discovered during verification.

2.2 Student Archetype Development

We developed four student archetypes based on empirical distributions in nursing education populations. Each archetype receives task-specific efficiency multipliers derived from peer-reviewed studies.

Archetype Justifications:

Fast Learners (20%): Students in the top performance quintile read 30-40% faster than average based on standardized reading assessments (Komarraju et al., 2013). They typically employ efficient study strategies, require minimal content repetition, and often secure housing near campus (0.80× commute). The 0.90× video multiplier reflects their use of 1.5-2× playback speeds.

Average Students (50%): The reference group representing median performance across all dimensions. All multipliers = 1.00× by definition.

Deep Processors (20%): Students with deep learning orientations spend significantly more time on tasks—not due to deficiency but due to thorough processing strategies (Biggs et al., 2001). They rewatch video segments (1.50× multiplier), extensively annotate readings (1.20× multiplier), and revise clinical documentation multiple times (1.10× multiplier).

ESL/Struggling Learners (10%): International and ESL students require approximately 50% more time for academic reading even at advanced English proficiency (Huang et al., 2020). The 1.50× reading multiplier aligns with documented 30 WPM gaps in medical contexts (Schmidtke et al., 2024). Extended commute times (1.20×) reflect higher public transportation dependence among international students.

2.3 Probability Distribution Parameters

Each task type was modeled as a normal distribution with parameters based on observed variability in educational settings:

Where:

• μ = base time from deterministic analysis (Table 1)
• σ = standard deviation calculated as CV × μ
• CV = coefficient of variation specific to task type

2.4 Monte Carlo Simulation Algorithm

We implemented a Monte Carlo simulation with n = 1,000 virtual students to model the population distribution. The algorithm proceeds as follows:

Step 1: Generate Student Population

Step 2: Add Individual Variation

To capture within-archetype variation, we add noise to each multiplier:

This creates approximately ±20% variation at 2σ within each archetype.

Step 3: Calculate Weekly Workload

For each student i and week w:

Step 4: Weekly Intensity Multipliers

Based on the original study's identification of high-intensity weeks:

2.5 Supply-Demand Analysis Framework

For each simulated student, we calculate:

Available Supply:

Variable Demand:

Individual Deficit/Surplus:

3. Results

The Monte Carlo simulation with 1,000 students revealed substantial heterogeneity masked by point estimates. Figure 1 displays the distribution of weekly workload during a representative mid-semester week (Week 7).

The mean workload of 91.4 hours significantly exceeds the deterministic estimate of 77.6 hours due to individual variation. The distribution shows strong positive skewness (γ₁ = 0.85), indicating a long right tail of students facing extreme workloads. Table 5 presents the critical comparison between available time (supply) and required time (demand) for each student archetype.

During Week 13, which includes final exams and project deadlines, the situation becomes more severe. Figure 2 displays peak week distribution with visible archetype separation.

Federal regulations specify maximum expected workload of 3 hours per credit per week. For 16 credits: Federal maximum: 48 hours/week and Federal ceiling (125%): 60 hours/week. Compliance analysis shows 100% of students exceed the 60-hour ceiling during peak periods.

Decomposing total workload by component reveals which tasks drive the greatest disparities. Reading shows the highest coefficient of variation (CV = 0.31) and the largest absolute disparity, with ESL learners spending 18.9 more hours per week on reading than fast learners (Table 8).

These findings indicate that under current modeling assumptions, the program workload is physiologically impossible for 100% of the student population. However, several variables could be fine-tuned through empirical data collection using a simple survey instrument distributed to the class. Such an instrument would capture actual commute times, self-ranked learning styles, ESL status and associated processing speeds, and individual efficiency variations, creating more accurate population distributions and archetype assignments. While this empirical refinement would improve model precision—particularly in accurately distributing students across archetypes and calibrating commute burdens—the core structural relationship between time demand and supply would remain unchanged. Given typical nursing cohort sizes (50-150 students), the sample would not be large enough to fundamentally alter the population means in a direction that would resolve the deficit. The mathematical constraints are too substantial: even optimistic recalibrations of efficiency parameters would require implausibly large shifts to bring any archetype into positive territory.

4. Discussion

4.1 The Myth of the Average Student

Our analysis reveals that designing programs for the "average" student—who requires 73.3 hours weekly—systematically excludes large portions of the student body. The mean obscures a distribution where:

• 20% of students (fast learners) can manage within available time
• 50% face moderate but manageable deficits through efficiency gains
• 30% confront physiologically impossible demands

This finding aligns with critiques of one-size-fits-all education models (Tomlinson et al., 2003) and validates calls for adaptive program design.

4.2 Physiological Impossibility at the Tail

The 95th percentile students requiring 115.3 hours during peak week face a mathematical impossibility. With 168 weekly hours:

• 115.3 hours for academics
• 49 hours for sleep (7 hrs/night minimum)
• Subtotal: 164.3 hours
• Remaining for meals, hygiene, commute: 3.7 hours total

Research demonstrates that sleep restriction to <6 hours for two weeks produces cognitive impairment equivalent to 48 hours of total sleep deprivation (Van Dongen et al., 2003). Students attempting to function on 5 hours of sleep would be clinically impaired while providing patient care—an unacceptable safety risk.

4.3 Structural Inequity and Selection Bias

The workload distribution creates a hidden selection mechanism. Students who succeed likely possess:

• Above-average processing speed (reducing task time)
• English as native language (avoiding 1.5× reading penalty)
• Proximity to campus (minimizing commute)
• Financial support (eliminating work obligations)
• Robust physical health (tolerating sleep deprivation)

This selection bias perpetuates healthcare workforce homogeneity precisely when patient populations demand culturally and linguistically diverse providers (Sullivan Commission, 2004).

4.4 Statistical Robustness and Parameter Sensitivity

While empirical data collection through survey instruments could refine our parameter estimates, the mathematical structure of our findings demonstrates robustness to reasonable calibration adjustments. A survey instrument distributed to the actual nursing cohort would fine-tune measurables such as:

• Actual commute times and transportation methods
• Self-ranked learning styles and processing preferences
• ESL status and associated reading speed challenges
• Individual efficiency variations and study habits
• Technology proficiency affecting video processing speed

However, typical nursing cohort sizes (50-150 students) would not provide sufficient sample size to shift population parameters enough to reverse the fundamental deficit. Consider the constraints:

Even if survey data revealed more favorable distributions—such as 40% fast learners instead of 20%, or average commute times of 20 minutes rather than 45 minutes—these adjustments would improve population means by only 3-5 hours. The core structural relationship between the 77.6-hour weekly demand and 63.3-hour weekly supply cannot be overcome through parameter refinement alone.

With realistic nursing cohort sizes, the standard error around empirically-derived means would be SE = σ/√n ≈ 14.8/√100 = 1.48 hours. For survey data to invalidate our conclusions, it would need to demonstrate that our base assumptions were off by 15-20 hours per week—an implausibly large calibration error that exceeds 10-13 standard errors.

4.5 Limitations

Several constraints limit our analysis:

• Independence assumption: We modeled tasks independently, though fatigue likely creates negative correlations
• Normal distributions: Some tasks may follow skewed distributions
• Static multipliers: Student efficiency likely varies with fatigue and stress
• Behavioral adaptation: Students may employ coping strategies not captured in our model
• Task count discrepancy: The foundational deterministic analysis contained methodological errors, inflating task counts by 2.8× (558 vs. 197 actual tasks). While this does not affect time-based calculations, it raises questions about analytical rigor in the original study
• Parameter estimation: Our efficiency multipliers are based on literature estimates rather than direct observation of this student population. A survey instrument could refine these parameters by measuring actual commute times, self-ranked learning styles, ESL processing speeds, and individual efficiency variations. However, typical nursing cohort sizes (50-150 students) would not provide sufficient statistical power to overcome the 14.3-hour structural deficit through parameter adjustment alone

Future research should incorporate dynamic modeling with fatigue effects and validate predictions through time-diary studies with the actual student cohort.

5. Conclusions

This Monte Carlo analysis reveals that under our modeling assumptions, 100% of students face time deficits that exceed available hours after accounting for basic physiological needs. While confirming the mean requirement of 91.4 hours weekly, we find that this represents a mathematical impossibility for all student archetypes within the 63.3 hours available for independent study.

The analysis demonstrates that the program structurally requires more time than available after basic physiological needs across all student populations:

• Fast learners face 11.8-hour weekly deficits
• Average students confront 26.0-hour weekly deficits
• ESL and struggling learners face 47.7-hour weekly deficits

These findings indicate that under current modeling assumptions, the program workload is physiologically impossible for 100% of the student population. However, several variables could be fine-tuned through empirical data collection using a simple survey instrument distributed to the class. Such an instrument would capture actual commute times, self-ranked learning styles, ESL status and associated processing speeds, and individual efficiency variations, creating more accurate population distributions and archetype assignments.

While this empirical refinement would improve model precision—particularly in accurately distributing students across archetypes and calibrating commute burdens—the core structural relationship between time demand and supply would remain unchanged. Given typical nursing cohort sizes (50-150 students), the sample would not be large enough to fundamentally alter the population means in a direction that would resolve the deficit. The mathematical constraints are too substantial: even optimistic recalibrations of efficiency parameters would require implausibly large shifts to bring any archetype into positive territory.

For example, if survey data revealed that 40% of students are fast learners (rather than our assumed 20%), this would improve the population mean but would not change the fundamental finding that fast learners themselves face an 11.8-hour deficit. Similarly, more precise commute data might reduce individual variation but cannot overcome the 14.3-hour structural deficit inherent in the program design.

References