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?