Tutorial Statistika (distribusi Normal dengan Tabel Z)

Introduction

This tutorial provides a step-by-step guide on calculating the areas of rice fields with productivity above 8 tons and below 5 tons, using the properties of a normal distribution and Z-tables. The total area is 100,000 hectares, with an average productivity of 6 tons per hectare and a standard deviation of 0.9 tons. Understanding these calculations is essential for agricultural planning and productivity analysis.

Step 1: Understand the Normal Distribution

• The normal distribution is a probability distribution that is symmetric about the mean.

• Key parameters:

  • Mean (μ): The average value (6 tons in this case).
  • Standard Deviation (σ): Measures the dispersion (0.9 tons here).

• The Z-score formula helps determine how far a value is from the mean in terms of standard deviations:

  Z = (X - μ) / σ
  

• Where:

  • Z is the Z-score.
  • X is the value of interest.

Step 2: Calculate the Z-scores

1. Calculate the Z-score for 8 tons:

   • Substitute values into the Z-score formula:

     Z = (8 - 6) / 0.9
     

   • Calculate:

     • Z = 2.22 (rounded to two decimal places)

2. Calculate the Z-score for 5 tons:

   • Substitute values into the Z-score formula:

     Z = (5 - 6) / 0.9
     

   • Calculate:

     • Z = -1.11 (rounded to two decimal places)

Step 3: Use the Z-table to Find Areas

• A Z-table shows the area under the curve to the left of a given Z-score.
• Look up the Z-scores calculated:
  • For Z = 2.22, the area is approximately 0.9861.
  • For Z = -1.11, the area is approximately 0.1335.

Step 4: Calculate the Area Between the Z-scores

• To find the area of rice fields producing between 5 and 8 tons:

  • Subtract the area for Z = -1.11 from the area for Z = 2.22:

    Area = 0.9861 - 0.1335
    

  • Calculate:

    • Area ≈ 0.8526 (or 85.26% of the total area).

Step 5: Determine the Total Area of Interest

• To find the actual area of rice fields:

  • Multiply the percentage area by the total area:

    Total Area = 0.8526 * 100,000 Ha
    

  • Calculate:

    • Total Area ≈ 85,260 Ha.

Conclusion

In this tutorial, we explored how to calculate the areas of rice fields with specific productivity levels using normal distribution and Z-tables. Key steps included calculating Z-scores, using the Z-table for areas, and then determining the total area of interest based on those calculations.

Next steps could involve applying these methods to different datasets or exploring further statistical analysis related to agricultural productivity.