A probability distribution describes how the possible values of a random quantity are spread. This chapter covers two: the binomial distribution, for counting successes, and the normal distribution, for measurements on a continuous scale.
The chapter sits inside the SPM Additional Mathematics guide. The binomial formula uses nCr, so the permutations and combinations chapter is a useful base.
How do the skills fit together?
The chapter has two branches, and the first step of any question is choosing the branch.
Binomial branch.
- Recognising binomial conditions
- Calculating binomial probabilities
- Finding mean and variance of a binomial variable
Normal branch.
- Standardising a normal random variable
- Reading normal-distribution tail probabilities
- Finding unknown normal-distribution parameters
A short orienting example
A teacher sets 10 true-or-false questions and a student guesses every one. The count of correct answers is a number from 0 to 10, found by repeating a yes-or-no trial 10 times. This is a binomial situation.
Now the same class is weighed. A student’s mass is measured on a continuous scale, so it can take any value in a range, and the bell-shaped normal curve is the right model.
The rule of thumb: counting a fixed number of trials points to binomial, and measuring a quantity on a scale points to normal. The page on probability model selection under constraints practises this choice.
Who should start where?
Match your situation to a starting point:
- If you are unsure when to use binomial, start with recognising conditions.
- If your binomial setup is right but your answers are off, go to calculating probabilities.
- If z-scores and tables confuse you, begin with standardising.
- If you want to test yourself, use the probability distributions practice set.
The word-problem structure worksheet helps break a long story into parts. For a teacher who can work through mixed questions with you, see online one-to-one Additional Mathematics tuition.