CIE A Level Maths: Probability & Statistics 1复习笔记3.3.3 Normal Distribution - Calculations
Normal Distribution - Calculations
Calculating Normal Probabilities
How do I find probabilities using a normal distribution?
It is likely that your calculator has a function that can find normal probabilities, if so it is a good idea to learn to use it so that you can check your probabilities
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- However you must show your calculations to get the z values and use the tables to get all the marks
How do I calculate the probability for a normal distribution?
Worked Example
Inverse Normal Distribution
Given the value of P(X < a) or P(X > a) how do I find the value of a?
- Given a probability you will have to look through the table of the normal distribution to locate the z-value that corresponds with that probability
- Look at whether your probability is greater or less than 0.5 and the direction of the inequality to determine whether your z-value will be positive or negative
You do not need to remember these, a sketch will help you see it
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- Always sketch a diagram
- If your probability is less than 0.5 you will need to subtract it from one to find the corresponding z value
- Remember that the position of the z-value will not change, only the direction of the inequality
Worked Example
Exam Tip
- The most common mistake students make when finding values from given probabilities is forgetting to check whether the z-value should be negative or not. Avoid this by checking early on using a sketch whether z is positive or negative and writing a note to yourself before starting the other calculations.
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