Normal distribution (AI SL 4.9)
Normal distribution
Scenario: The Enigma of the Dragon's Flight
Background:
In the mystical land of Draconia, dragons are the main mode of transportation. According to ancient lore, a fully-grown dragon has an average flight speed of 200 km/h with a standard deviation of 120 km/h. However, recent reports suggest that dragons are flying slower than usual, and the king has tasked you with investigating these claims.
Objective:
As the kingdom's Master of the Dracometrics, your role is to use the principles of the normal distribution to analyze the flight speeds of dragons and determine if they are indeed flying slower on average.
Investigation Steps:
1. Hypothesis Setting:
- Null Hypothesis (H0): The average flight speed of dragons is 200 km/h (μ = 200).
- Alternative Hypothesis (H1): The average flight speed of dragons is less than 200 km/h (μ < 200).
2. Data Collection:
- You decide to measure the flight speed of a sample of dragons during their routine flights.
- The speeds will be recorded and analyzed.
3. Statistical Analysis:
- Use the normal distribution N(200, 120^2) to model the flight speeds.
- Calculate the probabilities associated with various observed speeds.
- Determine the z-scores for the speeds that are significantly lower than the mean.
4. Decision Making:
- Based on the probabilities and z-scores, conclude whether the dragons are flying slower than usual.
- Consider the natural variability expressed by the standard deviation when making your decision.
Questions for Investigation:
1. Discovery Question:
- What factors could contribute to a decrease in the dragons' average flight speeds?
2. Understanding the Normal Distribution:
- How does the standard deviation affect the shape of the normal distribution curve?
3. Implications of Findings:
- If dragons are indeed flying slower, what could be the potential impact on the kingdom's transportation and economy?
4. Reflection:
- Why is it important to consider the entire distribution of speeds rather than just the average when assessing the dragons' performance?
- How might your findings influence policy decisions in Draconia?
