IB DP Maths: AA HL復(fù)習(xí)筆記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
- 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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