Math, asked by nakuldotasara, 18 hours ago

. An ice-cream parlour receives a customer at an average rate of 4 per minute. If the number of customers received by the parlour follows a Poisson distribution, what is the approximate probability that 16 customers will be coming to the parlour in a particular 4-minute period on a given day?​

Answers

Answered by amitnrw
6

Given  An ice-cream parlour receives a customer at an average rate of 4 per minute.

If the number of customers received by the parlour follows a Poisson distribution,  

To Find :  the approximate probability that 16 customers will be coming to the parlour in a particular 4-minute period on a given day

Solution:

an average rate of 4 per minute.

=> an average rate of 4* 4  per  4 minute.

=> an average rate of 16  per  4 minute.

Hence mean = 16

λ = 16 ≈

P(x)  = λˣ  e^(-λ) / x!

P(16) = 16¹⁶e⁻¹⁶/16!

= 0.099

≈ 0.1

approximate probability that 16 customers will be coming to the parlour in a particular 4-minute period on a given day  ≈ 0.1

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