Finding probabilities involving Z scores

Example 10Find the area between Z = –2.51 and Z = 2.575P( –2.51 < z < 2.575If we want to find the probability of selecting one number from the z distribution and having thatnumber be BETWEEN the z value of –2.51 the z value of 2.575 we need to find the areaBETWEEN z = 2.51 and z = 2.575z = –2.51z = 2.575Positive Z Scoresthe area to the left of Z = 2.575 is .9950Standard Normal (Z) Distribution: Cumulative Area to the LEFT of ZZ scores of 3.5 or more use .9999 AREA Z Score AREA Z Score0.9500 1.645 0.9950 2.575Negative Z Scoresthe area to the left of Z = –2.51 is .0060Standard 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 0.0048If the area to the left of Z = 2.575 is 0.9950and the area to the left of Z = –2.51 is 0.0060then the area BETWEEN Z = 2.575 and Z = –2.51 is.9950 – .0060= .9890P( –2.51 < z < 2.575 ) = .9890Section 6 – 3B Lecture Page 16 of 16 © 2012 Eitel