Finding the Probability of Z > 1.52

The probability of Z being greater than 1.52?Remember that the total area under the curve equals 1 0.9357 Area we want Z  = 0 1.52 P(Z >1.52) = 1 – P(Z < 1.52) = 1 - 0.9357= 0.0643

P(-0.9 < Z < 1.52) = ? Area we want Z  = 0 -0.9 1.52 How do we use the normal table to find this area?

First, we obtain the area less than 1.52 P( Z < 1.52) = ? We already know that this is0.9357 Area less than 1.52 is more than we want Need to subtract the area less than -0.9 Z  = 0 -0.9 1.52 How do we use the normal table to find this area?

How do we use the normal table to find this area? P(-0.9< Z < 1.52) = P(Z < 1.52) – P(Z < -0.9) = 0.9357 – 0.1841 Area less than 1.52 is more than we want Need to subtract 0.1841 - the area less than -0.9 Z  = 0 -0.9 1.52

P(-0.9< Z < 1.52) = P(Z < 1.52) – P(Z < -0.9) = 0.9357 – 0.1841 = 0.7516 0.7516 Z  = 0 -0.9 1.52

Standard Normal Distribution Z ~ N(0 , 1) P(Z < Za) = 0.025 Z  = 0 Za

Standard Normal Distribution Z ~ N(0 , 1) P(Z < -1.96) = 0.025 Z  = 0 -1.96 Therefore, Za = -1.96

Standard Normal Distribution Z ~ N(0 , 1) BUT, how do we get areas under thecurve for other normal distributions? Normal Distribution X ~ N( , 2) Answer Transform X into Z! Z 0 X 

Finding the Probability of Z > 1.52