Skip to content

3.3.4 Examples

3.3.4 Examples

Rohit's Garage Example

Scenario: Rohit offers a discount if oil changes take longer than 20 minutes. He is interested in probabilities related to service times and the number of services completed.

Service Time Analysis:

  • Exponential Distribution: Average service time of 20 minutes.

Probability Calculations:

  • Less than 20 minutes: Uses cumulative probability function.

    • P(X < 20) = 1 - e^(-0.05 * 20) ≈ 0.632 (63% chance service is less than 20 minutes)

  • Between 15 and 30 minutes: Difference between cumulative probabilities at these points.

    • P(15 < X < 30) = e^(-0.05 * 15) - e^(-0.05 * 30) ≈ 0.249 (24.9% chance service takes 15-30 minutes)

Service Count Analysis

  • Four-hour Shift:

    • Expected number of oil changes: 12 (20 minutes each, so 3 per hour).
    • Probability of completing more than 15 oil changes modeled as Poisson with λ = 12.

  • Eight-hour Shift:

    • Expected number of oil changes: 24.
    • Probability of completing more than 30 oil changes modeled as Poisson with λ = 24.

Example Calculations

  • Morning shift output: P(Y > 15) with λ = 12 calculated using Poisson distribution.
  • Full day output: P(Y > 30) with λ = 24 calculated using Poisson distribution.
Ask Hive Chat Chat Icon
Hive Chat
Hi, I'm Hive Chat, an AI assistant created by CollegeHive.
How can I help you today?