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NeX [460]
3 years ago
8

The average number of customers arriving at an ATM machine is 27 per hour during lunch hours. Use equation to denote the number

of arrivals in a 5 minute time interval. Assume the customers arrive independently and the number of arrivals within each 5 minutes follows a Poisson distribution. Keep at least 4 decimal digits if the result has more decimal digits. The probability that exactly 2 customers arrive in a given 5 minute interval is closest to
Mathematics
1 answer:
Helga [31]3 years ago
4 0

Answer:

The probability that exactly 2 customers arrive in a given 5 minute interval =  0.2667

Step-by-step explanation:

Given -

The average number of customers arriving at an ATM machine is 27 per hour during lunch hours. then the average number of customers arriving at an ATM machine n a 5 minute time interval = \frac{27}{60} \times 5 = 2.25

average number of customers arriving at an ATM machine n a 5 minute time interval (\lambda ) = 2.25

Let X denote the no of customer arrivals in a 5 minute time interval

The probability that exactly 2 customers arrive in a given 5 minute interval =

P( X = 2 )  = \frac{e^{-\lambda }\lambda ^{X}}{X!}            ( Using poision distribution )

               =  \frac{e^{-2.25} (2.25)^2}{2!}

               = \frac{.1054 \times 5.0625}{2}

               =   0.2667

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