Skip to content

Salam Academy

Sign in Create account

LearnAQA7357First teaching 2017Paper 3 · Pure and StatisticsStatistical distributions

Paper 3 · Module

Statistical distributions

5 subtopics≈ 175 min in total

Start the module: Probability distributions Open graphing calculator

Probability distributions
A random variable turns the outcome of an experiment into a number. Listing each possible value with its probability gives a distribution table, and the probabilities must add up to $1$ .
≈ 30 min
The binomial distribution
Count the successes in $n$ independent trials, each with the same chance $p$ . The probability of exactly $r$ successes is $\binom nr p^r(1-p)^{n-r}$ : choose which trials succeed, then multiply.
≈ 40 min
Standardising and normal probabilities
Heights, masses and exam marks often follow a symmetric bell-shaped curve. Every normal distribution is the standard one, $Z\sim N(0,1)$ , shifted and stretched, so one table of $\Phi(z)$ answers every question.
≈ 35 min
Inverse normal and finding μ and σ
Run the standardising formula backwards. Turn the probability into a $z$ -value with the tables, then solve $\dfrac{x-\mu}{\sigma}=z$ for whichever quantity is missing.
≈ 35 min
Normal approximation to the binomial
For large $n$ , the binomial's bars trace out a bell curve. Replace $B(n,p)$ by $N(np,npq)$ , widen each whole number into an interval of width $1$ (the continuity correction), and standardise.
≈ 35 min