Finding Unknown Parameters (DP IB Analysis & Approaches (AA)): Revision Note

Finding sigma and mu

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

• If the mean or standard deviation of  is unknown then you will need to use the standard normal distribution

• You will need to use the formula

  • or its rearranged form 

• You will be given a probability for a specific value of

  • or 

• To find the unknown parameter:
  

• STEP 1
  Sketch the normal curve

  • Label the known value and the mean

• STEP 2
  Find the z-value for the given value of x

  • You will know or 

  • Use the Inverse Normal Distribution to find the value of such that or 

    • Make sure the direction of the inequality for matches the inequality for 

  • Try to use lots of decimal places for the z-value or store your answer to avoid rounding errors

    • You should use at least one more decimal place within your working than your intended degree of accuracy for your answer

• STEP 3
  Substitute the known values into or 

  • You will be given one of the parameters (μ or σ) in the question

  • You will have calculated z in STEP 2

• STEP 4
  Solve the equation to find the missing parameter

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

  • You can form two equations (rearranging to the form  is helpful)

  • You now have to solve the two equations simultaneously (you can use your calculator to do this)

  • Be careful not to mix up which z-value goes with which value of x