IB DP Maths: AA SL复习笔记4.6.3 Standardisation of Normal Variables
Standard Normal Distribution
What is the standard normal distribution?
- The standard normal distribution is a normal distribution where the mean is 0 and the standard deviation is 1
Why is the standard normal distribution important?
- Any normal distribution curve can be transformed to the standard normal distribution curve by a horizontal translation and a horizontal stretch
z-values
What are z-values (standardised values)?
Finding Sigma and Mu
How do I find the mean (μ) or the standard deviation (σ) if one of them is unknown?
How do I find the mean (μ) and the standard deviation (σ) if both of them are unknown?
- If both of them are unknown then you will be given two probabilities for two specific values of x
- The process is the same as above
- You will now be able to calculate two z -values
You now have to solve the two equations simultaneously (you can use your calculator to do this)- Be careful not to mix up which z-value goes with which value of x
Worked Example
It is known that the times, in minutes, taken by students at a school to eat their lunch can be modelled using a normal distribution with mean μ minutes and standard deviation σ minutes.
Given that 10% of students at the school take less than 12 minutes to eat their lunch and 5% of the students take more than 40 minutes to eat their lunch, find the mean and standard deviation of the time taken by the students at the school.
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