5.2 The Standard Normal Distribution

         Graph                                        

 Density Curve - graph of a continuous probability distribution

      1.  Total area is 1
      2.   Height at all points between 0 & 1

Uniform Density Curves  -

#2
 

#4
 

Normal Density Curves
     In this section STANDARD mean = 0  and standard deviation = 1

     Real usefulness is later for different means and standard Deviations

     Note Picture pg. 231  comparing male & female heights

Given z-scores, find probabilities
      P(0 < z <1)                                         
 

      P(z > .5)                                         
 

      P(-1.2 < z < 0)                                 
 

      P(-1.2 < z < .4)                                         
 

      P(1 < z < 1.75)                                                    
 

      P(z < -2)                                                 
 
 
 

 Examples:  Some of #6-#24 even
 
 
 
 

Empirical Rules
       Within 1 Standard Deviation             P(-1 < z < 1)
                                                                             

        Within 2 Standard Deviations            P(-2 < z < 2)                                     
                                                                                                 
        Within 3 Standard Deviations         P(-3 < z < 3)
                                                                                                 
 

      68% within 1S.D.,  95% within 2 S.D.,  99.7 within 3 S.D. from chapter 2
 

     If Random Variable is Continuous     P(z = a) = 0        
                    *** Note difference from Discrete
 

Note:   z scores are positive or negative, but Probabilities are from 0 to 1
 
 

Given Probability, find z-score:  Often probabilities are given as percents

 #30  Find P30                                                 
 
 

 #32                                                                                
 
 
 

#36