IB DP Maths: AA SL复习笔记4.6.2 Calculations with Normal Distribution

How do I find probabilities using a normal distribution?

How do I calculate P(X = x): the probability of a single value for a normal distribution? 

How do I calculate P(a < X < b): the probability of a range of values for a normal distribution?

• You need a GDC that can calculate cumulative normal probabilities
• You want to use the "Normal Cumulative Distribution" function
  • This is sometimes shortened to NCD, Normal CD or Normal Cdf
• You will need to enter:
  • The 'lower bound' - this is the value a
  • The 'upper bound' - this is the value b
  • The 'μ' value - this is the mean
  • The 'σ' value - this is the standard deviation
• Check the order carefully as some calculators ask for standard deviation before mean
  • Remember it is the standard deviation
    • so if you have the variance then square root it
• Always sketch a quick diagram to visualise which area you are looking for

How do I calculate P(X > a) or P(X < b) for a normal distribution? 

Are there any useful identities? These are useful when:

• • The mean and/or standard deviation are unknown
  • You only have a diagram
  • You are working with the inverse distribution

Given the value of P(X < a) how do I find the value of a?

• Your GDC will have a function called "Inverse Normal Distribution"
  • Some calculators call this InvN

Given the value of P(X > a)  how do I find the value of a?