Answer:
 =2.6984126984 
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
 [/tex]
[/tex]
Step-by-step explanation:
The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence

the generating function would be

we can multiply P(x) by x to get
 
 
Note that

which for  can be rewritten as
 can be rewritten as 

 
        
             
        
        
        
This can be represented by the expression 4d.
 
        
             
        
        
        
Answer:
Step-by-step explanation:
Both 115 and 145 mph are above the mean.  Draw a normal curve and mark these speeds.  115 mph is 1 standard deviation above the mean; 130 would be 2 standard deviations above the mean; and 145 would be 3 s. d. above it.
We need to find the area under the standard normal curve between 115 and 145.  This is equivalent to the area under the standard normal curve between z = 1 and z = 3.
I used my TI-83 Plus calculator's DISTR function "normalcdf(" to calculate this area:  normalcdf(1, 3) = 0.1573.
The area between z = 1 and z = 3 is 0.1573.  In other words, the percentage of serves that were between 115 and 145 mph was 15.73%.