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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