13 2cndtable

Cumulative Normal Distribution (CND) Table

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To find probabilities using the Standard Normal Distribution: $Z \sim N \big(0, \; 1\big)$

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Example 1 (2 decimal places)

Find $Pr\big(Z < 0.43\big)$

Solution

  • Go down the left column to find 0.4 (1st decimal place)
  • Move across to find column labelled 3 (2nd decimal place)
  • Hence
    • $Pr\big(Z < 0.43\big) = 0.6664$
13.2cndtbl.gif

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Example 2 (3 decimal places)

Find $Pr\big(Z < 0.934\big)$

Solution

  • Go down the left column to find 0.9 (1st decimal place)
  • Move across to find column labelled 3 (2nd decimal place)
    • This gives $Pr\big(Z < 0.93\big) = 0.8238$
  • Then look up the mean difference(right section of table) for 4 (3rd decimal place)
    • The appropriate mean difference is 10,
  • so add 10 to the 4th decimal place of the value we got from step 2 (ie add 0.0010)
  • Hence $Pr\big(Z < 0.934\big) = 0.8248$

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