The answer would be 52.7.5
        
             
        
        
        
Answer:
 
  
Where  and
 and 
Since the distribution for X is normal then the distribution for the sample mean  is also normal and given by:



So then is appropiate use the normal distribution to find the probabilities for 
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  The letter  is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words:
 is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: 
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
 
  
Where  and
 and 
Since the distribution for X is normal then the distribution for the sample mean  is also normal and given by:
 is also normal and given by:



So then is appropiate use the normal distribution to find the probabilities for 
 
        
             
        
        
        
Answer:
A is estimated to 110.11
Step-by-step explanation:
Area of a regular pentagon = pa/2
p= perimeter
a= the apothem
Calculate it from the side length: p= 5s
 
        
             
        
        
        
Answer:
(x,y)=(0,7.333)
Step-by-step explanation:
We are required to:
Maximize p = x + 2y subject to
- x + 3y ≤ 22
- 2x + y ≤ 14
- x ≥ 0, y ≥ 0.
The graph of the lines are plotted and attached below.
From the graph, the vertices of the feasible region are:
At (0,7.333), p=0+2(7.333)=14.666
At (4,6), p=4+2(6)=4+12=16
At (0,0), p=0
At (7,0), p=7+2(0)=7
Since 14.666 is the highest, the maximum point of the feasible region is (0,7.333).
At x=0 and y=7.333, the function p is maximized.