CIE A Level Maths: Probability & Statistics 1復(fù)習(xí)筆記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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