Study Notes
The normal distribution is used to model continuous random variables and is represented by a symmetrical bell-shaped curve. It is defined by the mean (μ) and standard deviation (σ), and probabilities can be calculated using normal distribution tables.
- Continuous Random Variable — a variable with uncountable values related to real numbers.
Example: The time taken to do a test. - Probability Density Function (PDF) — a function representing the probability distribution of a continuous random variable.
Example: A graph based on a histogram shape. - Normal Curve — a symmetrical bell-shaped curve representing a normal distribution.
Example: Mean = median = mode. - Standard Normal Distribution — a normal distribution with a mean of 0 and standard deviation of 1.
Example: Z ~ N(0,1). - Continuity Correction — an adjustment made when approximating a discrete distribution with a continuous one.
Example: X = 13 is treated as 12.5 ≤ X ≤ 13.5.
Exam Tips
Key Definitions to Remember
- Continuous Random Variable
- Probability Density Function (PDF)
- Normal Curve
- Standard Normal Distribution
- Continuity Correction
Common Confusions
- Confusing the mean with the median and mode in a normal distribution.
- Forgetting to apply continuity correction when using normal approximation for binomial distribution.
Typical Exam Questions
- What is the probability that a continuous random variable X is greater than a certain value? Use the normal distribution table to find P(X > x₁).
- How do you find the z-score for a given value of X? Use the formula z = (X - μ) / σ.
- How is a binomial distribution approximated by a normal distribution? Use N(np, np(1-p)) with continuity correction.
What Examiners Usually Test
- Understanding and using the normal distribution table.
- Calculating probabilities for normal distributions.
- Applying the normal approximation to the binomial distribution.