Level 5 · Mathematics M5.7

Probability distributions and inference

Model random events with distributions, and test claims using samples.

Planned. This book is not written yet. Below is its plan, which a teacher can already use.

You are ready for this book if

You can expand (p + q)³ and find a probability with a tree diagram.

  • This book M5.7 Probability distributions and inference
  • One step down M4.7 Statistics

The plan

  1. M5.7.1 Random variables
    • Make a probability table for a discrete random variable
    • Find the expected value of a random variable
  2. M5.7.2 Variance and standard deviation
    • Find the variance and standard deviation of a data set
    • Find the variance of a random variable
  3. M5.7.3 The binomial distribution
    • Say when a binomial model fits a situation
    • Find P(X = 3) for a binomial distribution
    • Find the mean and variance of a binomial distribution
  4. M5.7.4 The normal distribution
    • Describe the bell shape of a normal distribution
    • Find probabilities using a normal model
    • Use the rule that about 95% lies within 2 standard deviations
  5. M5.7.5 Samples and the sample mean
    • Explain why sample means vary less than single values
    • Find the standard deviation of a sample mean
  6. M5.7.6 Testing a claim
    • Set up a null and an alternative hypothesis
    • Test a claim about a binomial probability at the 5% level
  7. M5.7.7 Testing a mean
    • Test a claim about a mean using a normal model
    • Explain the two ways a test can give the wrong answer
  8. M5.7.8 Correlation and regression
    • Find and read a correlation coefficient
    • Find a regression line and use it with care

For parents and teachers

Level 5 fits learners who can already: read a textbook. use functions and graphs. In many schools that is about 17 to 20, but start wherever the learner is.

Strand: Data and chance. Written and drawn by attnom. Free to read, print and share.