The binomial and normal distributions
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Two shapes that describe chance
- The binomial conditions
- Binomial probabilities
Read the transcript of the teaching part
Last time
Before we start: last time, in Probability distributions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Two shapes that describe chance
Count how many of sixteen students own a car. That is a count of successes, which follows the binomial distribution. Measure the length of a metal rod. That is a measurement on a scale, which follows the normal bell curve. Between them they cover most of the statistics paper.
The binomial conditions
A fixed number of trials, n. Each trial has two outcomes, success or failure. The trials are independent, and the probability p of success is the same each time. Then X, the number of successes, has the distribution B of n, p.
Binomial probabilities
The probability of exactly r successes is n C r, times p to the r, times one minus p to the n minus r. The mean is n p and the variance is n p times one minus p. For sums like at least two, add the terms, or use one minus the complement.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Finding an unknown value.
The whole chapter: Probability, The Normal Distribution.
Chapter 5.4: Discrete random variables
- Probability distributions: by selection, from outcomes, and with unknowns 6 min
- The binomial and normal distributions 6 min
- Binomial and geometric distributions, and drawing a probability distribution 6 min
Also for A Level Maths 9709 Paper 5
Which topics come up most in A Level Maths 9709 Paper 5 past papers, counted from every paper since 2004.