AQA A Level Maths: Statistics复习笔记4.3.3 Standard Normal Distribution
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.
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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