SOLUTION: A secretary periodically checks to see how many of the 3 lines into the office are busy. Her findings for one week were the following: No Lines Busy/ Frequency 0/

Algebra ->  Probability-and-statistics -> SOLUTION: A secretary periodically checks to see how many of the 3 lines into the office are busy. Her findings for one week were the following: No Lines Busy/ Frequency 0/       Log On


   

Question 93999: A secretary periodically checks to see how many of the 3 lines into the office are busy. Her findings for one week were the following:
No Lines Busy/ Frequency
0/ 20
1/ 65
2/ 25
3/ 10
Let the random variable X be the number of lines busy. Find the probability distribution of X.
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!

A secretary periodically checks to see how many of the 
3 lines into the office are busy. Her findings for one 
week were the following: 
No Lines Busy/ Frequency
0/ 20
1/ 65
2/ 25
3/ 10 
Let the random variable X be the number of lines busy. 
Find the probability distribution of X.

No Lines Busy  Frequency     Probability      
     X           f(X)           p(X)    
     0            20       20/120 =   1/6 = .167
     1            65       65/120 = 13/24 = .542
     2            25       25/120 =  5/24 = .208
     3            10       10/120 =  1/12 = .083
Totals           120                       1.000     

Here's a histogram of that distribution:

                      
                         
Notice that if the base of each of those 4 rectangles 
is 1, then the area of all the rectangles together is 1.

Edwin