HOW MANY SALESMEN ARE REQUIRED IN YOUR STORE?

   

      You are running a grocery store.  From experience, you know 4.6 customers arrive per hour.  You want to serve all of them almost without wait (90%).  How many salespersons you require?
     In statistics, there is topic called 'Poisson distribution'.  A formula in that topic tells us that the probability of number of customers arriving in an hour.

     4.6-N - No. of customers arriving per hour.
     P(K) = e ^-N * N^K/K!
     P(K) - probability of K customers arriving per hour,
     K!  - Factorial K - K*(K-1)*(K-2) ... 1
     e - 2.71 ....Euler's constant.

     The chance of '0'customer to show up
     = e^-4.6 * 4.6 ^0/0!
     =e^-4.6 *1/1
     =2.71 ^-4.6 = 0.010

   Probability of '1' customer =e^-4.6*4.6^1/1!
                           = 0.046
for 2 customers   = 0.106
for 3 customers  = 0.163
for 4                     = 0.188
for 5                     = 0.173
for 6                     =0.132
for 7                     =0.087
adding all the probabilities, we get 0.905 or 90.5%.  That is, the chance for 0-7 customers to arrive in one hour is 90.5%.  And one customer requires at least 15 minutes of service.  You should be able to serve, seven customers in one hour.  7 customers require  7  *15 =105 minutes of services.
Divide 105 by 60 minutes because we are dealing with one hour time window.
  105/60 =1.75 or 2
Hence 2 salesmen are enough for your store.

     Using this principle, we can solve.
1. No. of operators required in a call center.
2. no. of bays required in a bus stand.
3. No. of counters required in a office.
    Scientifically or mathematically, we can solve many problems.  But we always take decisions using our intuition.  It may be or may not be correct.    
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