Finding the mean and standard deviation, and the normal approximation to the binomial
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The teaching part (2 min) is free to watch. A free account opens the whole lecture: 6 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
- Work backwards from the percentages
- Standardising
- Two unknowns
Read the transcript of the teaching part
Last time
Before we start: last time, in Binomial and geometric distributions, and drawing a probability distribution, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Work backwards from the percentages
Usually you are given the mean and standard deviation and asked for a probability. Here it is the other way. You are told some probabilities, and asked to find the mean and the standard deviation. The route is inverse normal, then standardise. And when the variable is a binomial count with many trials, you can use a normal curve as a fast approximation, with a correction.
Standardising
z equals x minus mu, over sigma. It turns any normal value into a standard normal value. Going backwards, the z value comes from the inverse normal function on your calculator, given the probability to the left. Be careful with the side: if the area is to the right, use one minus that area.
Two unknowns
90 percent of heights are below 182.7. The z for 0.9 is 1.282. So 182.7 minus mu equals 1.282 sigma. 40 percent are below 162.5. The z for 0.4 is minus 0.253. So 162.5 minus mu equals minus 0.253 sigma. Subtract the two equations: 20.2 equals 1.535 sigma. So sigma is 13.2, and mu is 165.8.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Finding the mean and standard deviation · Finding the standard deviation · Normal approximation to the binomial.
The whole chapter: The Normal Distribution.
Chapter 5.5: The normal distribution
- Finding the mean and standard deviation, and the normal approximation to the binomial 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.