Problem 1 As Of March 22, 2020, Slovenia Reported A Total ✓ Solved

Problem 1 As of March 22, 2020, Slovenia reported a tota

Problem 1 As of March 22, 2020, Slovenia reported a total of 414 cases of COVID-19, of which 412 have been classified by both gender and age range. The data is summarized in the table below. Use this table to answer the questions below. Before doing so, fill in the missing totals in this table, then answer: a) What is the percentage of female COVID-19 cases? b) What is the percentage of COVID-19 cases in the age range from 35 to 74? c) What percentage of female COVID-19 cases are younger than 60 years? d) What percentage of the 15 to 34-year-old COVID-19 cases are men? e) According to this data, which age group has the lowest risk? Which gender has the highest risk? Is there a particular age and gender combination that is the riskiest group? Give reasons for your answers and show any computations.

Problem 2 Using SAT score distributions for 2019 high school graduates (mean and standard deviation for Composite, EBRW, and Math), create cutoff scores for the top 10.2% composite and top 4.09% math percentiles, showing computations using z-scores. a) Create a table of cutoff scores for each score type and explain how they meet the guidelines. b) Write a short memo to a supervisor introducing the table of cutoff scores. c) If only one cutoff can change — either lower the Math cutoff by 50 points or the Composite cutoff by 75 points — compute the new percentages passed under each change, the increases from the original, and state which change yields the larger increase. Show computations.

Paper For Above Instructions

Overview

This paper answers the two-part assignment above. For Problem 1 (Slovenia COVID-19 cases) the original table referenced in the prompt was not provided in the cleaned instructions. To complete the requested computations I (A) describe the general method for computing percentages from a contingency-style table, (B) demonstrate filling totals and computing each requested percentage using a reconstructed illustrative table (clearly marked as an assumed example), and (C) explain interpretation for risk assessment. For Problem 2 (SAT cutoffs) I use published 2019 SAT descriptive statistics as the basis for z-score computations, show how to obtain cutoffs from percentiles, give a short memo, and compute the impact of two single-cutoff changes. All computations use the z-score formula z = (x - μ) / σ and standard normal percentiles (z-table) to convert between scores and probabilities (Wackerly et al., 2014; College Board, 2020).

Problem 1 — Method and Example Computation

Method: For any contingency table of cases by gender and age range:

• Fill row and column totals and grand total.
• Percent female = (female total / grand total) × 100%.
• Percent in a given age range = (age-range total / grand total) × 100%.
• Percent of female cases younger than 60 = (female cases in age groups with age < 60 / female total) × 100%.
• Percent of 15–34-year-old cases who are men = (male cases in 15–34 / total 15–34 cases) × 100%.
• Identify lowest-risk age group and highest-risk gender by comparing percentages or rates; a riskiest age/gender cell is the cell with the highest proportion relative to its subgroup or the highest cell count depending on the risk definition.

Illustrative table (assumed example). Because the original table was not included in the cleaned instructions, I demonstrate using a plausible completed table consistent with the given grand total of 414 and 412 classified by gender/age (two observations possibly missing classification):

Using the illustrative table above:

• a) Percentage female = (181 / 412) × 100% = 43.9% (rounded) (example computation).
• b) Percentage in 35–74 = (130 + 45) / 412 = 175 / 412 = 42.5%.
• c) Female cases younger than 60 = women in 0–14 + 15–34 + 35–59 = 10+80+70 = 160; percent = 160 / 181 = 88.4%.
• d) Percent of 15–34 cases who are men = male in 15–34 / total 15–34 = 110 / 190 = 57.9%.
• e) Lowest-risk age group by share of total cases: 0–14 with 4.4% (18/412); highest-risk gender: men with 56.1% (231/412). The riskiest age/gender cell by count is men 15–34 (110 cases), so that combination is the riskiest in this example.

Interpretation: The precise answers depend on the actual provided table; the method above shows how to fill totals and compute requested percentages. Where classification is incomplete (414 total but 412 classified), note missing data and report any assumptions used. Always show raw counts and the arithmetic used to derive percentages so the analysis is transparent (Moore & McCabe, 2005).

Problem 2 — SAT Percentile Cutoffs and Policy Change Analysis

Sources and assumptions: For 2019 national SAT descriptive statistics, I use College Board figures: mean composite μ_C = 1059, μ_EBRW = 531, μ_Math = 528. For standard deviations I use representative section SDs (σ_EBRW ≈ 101, σ_Math ≈ 104) and σ_C ≈ 210 for the composite (College Board, 2020). All percentile conversions use the standard normal table (z-table) and the z-score formula z = (x − μ)/σ (NIST, 2020).

Step a — Compute cutoffs for given percentiles

Top 10.2% composite: the percentile below the cutoff is 1 − 0.102 = 0.898. The z corresponding to 0.898 ≈ 1.28 (z-table). Cutoff x_C = μ_C + zσ_C = 1059 + 1.28(210) ≈ 1328.

Top 4.09% math: percentile below = 0.9591. z ≈ 1.75. Cutoff x_M = 528 + 1.75(104) ≈ 528 + 182 = 710.

Table of cutoffs (example):

These cutoffs meet the guideline because the z-to-percentile mapping ensures the given fraction of the population is above each cutoff when the scores are approximately normal (College Board, 2020; Wackerly et al., 2014).

Step b — Short memo to supervisor

Memo (intro): Attached is a concise table of cutoff scores derived from 2019 SAT score distributions to identify applicants who automatically advance. Cutoffs were computed by converting target top-percentiles to z-scores and back to test-scale scores using the section and composite means and standard deviations (methodology shown below). The resulting cutoffs are: Composite ≥ 1328 (top 10.2%) and Math ≥ 710 (top 4.09%).

Step c — Single-cutoff change analysis

Option 1: Lower Math cutoff by 50 points: new math cutoff = 710 − 50 = 660. z_new = (660 − 528)/104 = 1.27 → percentile below ≈ 0.898 → new top proportion ≈ 10.2% (i.e., the math pass rate increases from 4.09% to ≈10.2%, an increase of ≈6.11 percentage points).

Option 2: Lower Composite cutoff by 75 points: new composite cutoff = 1328 − 75 = 1253. z_new = (1253 − 1059)/210 = 0.924 → percentile below ≈ 0.822 → new top proportion ≈ 17.8% (increase from 10.2% to 17.8%, i.e., +7.6 percentage points).

Conclusion: Lowering the composite cutoff by 75 yields the larger increase in the proportion of applicants who automatically pass (+7.6 pts) versus lowering math by 50 (+6.11 pts). Accordingly, to maximize the number of applicants advanced by changing only one cutoff, adjust the composite cutoff (provided the university is comfortable with expanding the composite-qualified pool) (College Board, 2020; StatTrek, 2021).

Final notes on practice and visualization

In all Normal-distribution work: (1) draw the normal curve with both standard-deviation marks and the measurement scale labeled, (2) shade the area of interest, (3) convert between x and z using z = (x − μ)/σ, (4) use the z-table for percentages below z (or software/calculator for precision). Visual tools (Khan Academy, StatTrek, NIST) aid verification (Khan Academy, 2021; NIST, 2020).

References

• College Board. (2020). SAT Suite of Assessments Annual Report 2019. College Board. https://reports.collegeboard.org/
• Wackerly, D., Mendenhall, W., & Scheaffer, R. (2014). Mathematical Statistics with Applications (7th ed.). Cengage Learning.
• Moore, D. S., & McCabe, G. P. (2005). Introduction to the Practice of Statistics (5th ed.). W. H. Freeman.
• NIST/SEMATECH. (2020). Engineering Statistics Handbook: Normal Distribution. National Institute of Standards and Technology. https://www.itl.nist.gov/div898/handbook/
• Khan Academy. (2021). Normal distribution and z-scores. https://www.khanacademy.org/math/statistics-probability
• StatTrek. (2021). Normal Distribution Table and Calculator. https://stattrek.com/
• Centers for Disease Control and Prevention (CDC). (2020). COVID-19 Situation Report. https://www.cdc.gov/coronavirus/2019-ncov/index.html
• World Health Organization (WHO). (2020). Coronavirus disease (COVID-19) Situation Reports. https://www.who.int/emergencies/diseases/novel-coronavirus-2019
• Agresti, A. (2018). Statistical Methods for the Social Sciences (5th ed.). Pearson.
• Altman, D. G., & Bland, J. M. (1995). Statistics Notes: Absence of evidence is not evidence of absence. BMJ, 311(7003), 485.