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Case Study: City of Medville Uses Statistical Approach to Estimate Costs for Its Pilot Project

To encourage sports and fitness among students from kindergarten to 12th grade, the education department of the city of Medville, Pennsylvania, conceived a 12-month pilot project to provide special free training, nutrition, and sports gear to the students of a select 10 schools. The goal of this project was to cover 70% of the student population under the new program. The initial challenge was to figure out the funds required to run this project and also the plan to carry out the project work.

For scope management, the project management committee divided the student population in different age groups and estimated the cost for students in each age group. Table 1.2 depicts the various student age groups and the cost estimates.

Table 1.2 Estimated Project Cost for Various Student Age Groups

Student Age Group

Estimated Cost Per Student

Less than 10 years old

$2,000

10 to 15 years old

$5,000

More than 15 years old

$3,000

The project assumed that the total population of students (2,000 students) was normally distributed with a mean age of 12 and a standard deviation of 3. The following statistical calculations for normal distribution were used to make decisions.

Determine Target Age Group for Initial Project Pilot

For normal distribution,

  • 1 σ covers roughly 68% of the population, which implies 68% of the total 2,000 students fall in the age group 9 to 15 (12 +/– 3).
  • 2 σ covers roughly 95% of the population, which implies 95% of the total 2,000 students fall in the age group 6 to 18 (12 +/– 6).

Because the goal of the pilot project was to cover 70% of the student population, students in age group 6 to 18 were selected for the initial pilot.

Estimate Project Costs for the Target Age Group

The target age group contained student population from all three population bands listed in Table 1.2. Thus, cost estimates pertaining to those population bands or age groups had to be considered for calculating costs for the target age group (6 to 18 years old). The project figured it out using the Excel NORMDIST17 function as follows:

  • Percentage of target students belonging to age group under 10 years (6 to 10 years old) = NORMDIST (10, 12, 3, 1) – NORMDIST (6, 12, 3, 1) = 22.97%
  • Cost Allocation for 6- to 10-year old students = (2000 * 22.97% * 2000) = $918,970
  • Percentage of target students belonging to age group 10 to 15 years (10 to 15 years old) = NORMDIST (15, 12, 3, 1) – NORMDIST (10, 12, 3, 1) = 58.89%
  • Cost Allocation for 10- to 15-years-old students = (5000 * 58.89% * 2000) = $5,888,522
  • Percentage of target students belonging to age group over 15 years = 1 – (22.97% + 58.89%) = 18.14%
  • Cost Allocation for over 15-year-old students = (3000 * 18.14% * 2000) = $1,088,432
  • Total Estimated Cost for All Target Students for the Initial Pilot = $918,970 + $5,888,522 + $1,088,432 = $7,895,924
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