Question

Calls at a telephone switchboard occur at an average rate of 6 calls per 10 minutes. Suppose the operator leaves for a 5-minute coffee break. What is the probability that exactly two calls occur while the operator is away ?

Answer 1

Hai friend,


Question :- Calls at a telephone switchboard occur at an average rate of 6 calls per 10 minutes. Suppose the operator leaves for a 5-minute coffee break. What is the probability that exactly two calls occur while the operator is away ?
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solution:-

Here, given
calls per 10minutes = 6
so in 5 minutes, there will be 3 calls

Probability = no of probable outcomes /Total outcomes *100

=2/3*100

=66.7%
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Conclusion :-
2/3 is the probability that exactly two calls occur while the operator is away

hope helped!

Answer 2

Poission distribution is applicable.

Using the formula of poission distribution : here ,lambda =6/10, in this case t=5 so that,( lambda t)=3.

Hence the required probability p(2) is given by:

P(2)=e^3 3^2/2! = 3e^3= 0.2240.