Finding probabilities involving Z scores

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Example 2BFinding the area to the Right of a negative Z scoreFind P( z > – 1.02 )The area under the z curve that is to the right of a given z value represents the probability ofselecting one number from the z distribution and having that number be more than the z value.If we want to find the probability of selecting one number from the z distribution and having thatnumber be more than the z value of – 1.02 we need to find the area to the RIGHT of z = – 1.02the area to the left of z = – 1.02is .1539the area to the right of z = – 1.02is 1– .1539 = .8461left tail area= .1539right tail area= .8461z = – 1.02 0If the area to the Left of Z = – 1.02 is 0.1539then the area to the Right of Z = – 1.02 is 1 – .1539P( z > – 1.02 ) = 1 – 0.1539 = .8461Section 6 – 3B Lecture Page 6 of 16 © 2012 Eitel
Example 3Find the area to the left of a negative Z scoreA Special Case for z = – 2.575P( z < – 2.575 )If we want to find the probability of selecting one number from the z distribution and having thatnumber be less than the z value of – 2.575 we need to find the area to the left of z = – 2.575Two negative Z scores with 3 decimal places are used in this course. These two 3 decimal placevalues and the areas to the left of them are listed separately at the bottom of the table.Negative Z ScoresThe cells at the bottom of the negative z scores table show thatthe area to the left of Z = –2.575 is 0.0050Standard Normal (Z) Distribution: Cumulative Area to the LEFT of ZZ 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09–2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048Z scores of –3.5 or less use .0001 AREA Z Score AREA Z Score0.0500 –1.645 0.0050 –2.575This means that the area to the LEFT of z = – 1.86 is 0.0050P( z < – 2.575 ) = 0.0050Finding the area to the Right of a negative Z scoreP( z > – 2.575 )If we want to find the probability of selecting one number from the z distribution and having thatnumber be greater than the z value of – 2.575 we need to find the area to the right of z = – 2.575If the area to the Left of Z = – 1.02 is 0.0050then the area to the Right of Z = – 2.575 is 1 – .0050 = .9950P( z > – 2.575 ) = 1 – 0.0050 = .9950Section 6 – 3B Lecture Page 7 of 16 © 2012 Eitel
Page 1: Section 6 - 3B:Finding probabilitie
Page 4 and 5: Example 1BFinding the area to the R
Page 8 and 9: Example 4Find the area to the left
Page 10 and 11: Example 5Finding the area to the le
Page 12 and 13: Example 7Finding the area to the le
Page 14 and 15: Example 8Find the area between z =
Page 16: Example 10Find the area between Z =

Finding probabilities involving Z scores

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