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IB DP Maths: AA HL復習筆記4.6.3 Standardisation of Normal Variables

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月13日下午12:16

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 1Why 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
Therefore we have the relationship:z-values

What are?z-values (standardised values)?

This is given in the?formula booklet

z-values can?be used to compare values from different distributions

Finding Sigma and Mu

How do I find the mean (μ) or the standard deviation (σ) if one of them is unknown?

STEP 4:?Solve?the equation

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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