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AQA A Level Maths: Statistics復(fù)習(xí)筆記4.3.3 Standard Normal Distribution

Category: A-level課程, 教材筆記, 福利干貨 Date: 2022年8月9日下午6:14

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
- It is denoted by?Z

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:

Finding Sigma and Mu

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

You will be given x and one of the parameters (μ ?or σ) in the question

- You will have calculated z in STEP 2
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

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 standard deviation 4 minutes.

Given that 10% of students at the school take less than 12 minutes to eat their lunch, find the mean time taken by the students at the school.

4-3-3-standard-normal-distribution-we-solution

Exam Tip

These questions are normally given in context so make sure you identify the key words in the question. Check whether your z-values are positive or negative and be careful with signs when rearranging.

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