Skip to content

Sampling Distribution Calculator

Run Fullscreen

Edit in p5.js Editor

About This MicroSim

Time to test those skills! This calculator helps you work through sampling distribution probability problems step-by-step, showing you exactly how to find the standard error, calculate z-scores, and determine probabilities. It works for both sample means and sample proportions.

How to Use

  • Mode Toggle: Switch between Mean and Proportion calculations
  • Input Parameters: Click on any input box and type new values
  • Probability Type: Choose "Less than," "Greater than," or "Between"
  • Example Presets: Load the Light Bulbs or Polling examples from the textbook
  • Watch the Steps: Follow the three-step calculation process

Key Formulas Used

For Sample Means: [ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} ]

For Sample Proportions: [ z = \frac{\hat{p} - p}{\sqrt{p(1-p)/n}} ]

Lesson Plan

Learning Objective

Students will apply sampling distribution concepts to calculate probabilities involving sample means and proportions, using z-scores and normal distribution tables (Bloom's Taxonomy: Apply).

Pre-Activity Discussion

  • "If we know the population mean and standard deviation, how can we predict what sample means are likely to occur?"
  • "What does it mean to find P(sample mean < 1175)?"

Guided Practice

  1. Load the Light Bulbs Example: Population mean = 1200 hours, SD = 100 hours, n = 64
  2. Follow Step 1: Calculate SE = 100/sqrt(64) = 12.5
  3. Follow Step 2: Calculate z = (1175 - 1200)/12.5 = -2.00
  4. Follow Step 3: Find P(Z < -2.00) = 0.0228 (about 2.3%)

Practice Problems

Problem 1: A factory produces chips with mean weight 10g and SD 0.5g. For samples of n=25, what's the probability the sample mean exceeds 10.2g?

Problem 2: If 65% of voters support a candidate, what's the probability that a sample of 200 voters shows less than 60% support?

Extension Questions

  1. What happens to the probability if we increase the sample size?
  2. Why does the z-score get larger (in absolute value) when the sample size increases?
  3. In the polling example, explain why getting less than 50% in the sample is quite possible even when the true proportion is 52%.

Common Mistakes to Avoid

  • Using population SD instead of standard error
  • Forgetting to take the square root in the SE formula
  • Using z-table values incorrectly (greater than vs. less than)

Sylvia Says

Acorn for your thoughts? Notice how the three steps always follow the same pattern: (1) Find SE, (2) Calculate z, (3) Look up probability. Master this process and you've got a powerful tool for understanding how samples behave!