The Central Limit Theorem and confidence intervals
Watch the whole lecture free
Make a free account to watch every lecture to the end: 4 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.
That was the teaching part. The rest of this lecture is free with an account: 4 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.
No password needed now: we email you a link to set one. Already have an account? Sign in, then come back to this page.
The teaching part (1 min) is free to watch. A free account opens the whole lecture: 4 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
- A range, not a guess
- The Central Limit Theorem
Read the transcript of the teaching part
Last time
Before we start: last time, in Sampling, unbiased estimates and the distribution of the sample mean, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
A range, not a guess
A poll says forty-five percent plus or minus three. It does not claim exactly forty-five. It gives a range that is very likely to contain the true value. That range is a confidence interval, and the Central Limit Theorem is the reason the bell curve works for it.
The Central Limit Theorem
Take a random sample of size n from any distribution with mean mu and variance sigma squared. If n is large, the sample mean is approximately normal. Its mean is mu and its variance is sigma squared over n. The spread of the mean shrinks with the square root of n. That is why bigger samples give narrower intervals.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Confidence interval for a mean · Confidence interval for a proportion.
The whole chapter: Sampling and Estimation.
Chapter 6.4: Sampling and estimation
- Sampling, unbiased estimates and the distribution of the sample mean 7 min
- The Central Limit Theorem and confidence intervals 7 min
Also for A Level Maths 9709 Paper 6
Which topics come up most in A Level Maths 9709 Paper 6 past papers, counted from every paper since 2004.