Question

Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to per minutes. Complete parts six 10 a and b below. Click here to view page 1 of the table of Poisson probabilities.1 Click here to view page 2 of the table of Poisson probabilities.2 Click here to view page 3 of the table of Poisson probabilities.3 Click here to view page 4 of the table of Poisson probabilities.4 Click here to view page 5 of the table of Poisson probabilities.5 a. Determine the probability that in a given 10 minute segment, three customers will arrive at the ATM. The probability is . (Round to four decimal places as needed.) b. What is the probability that fewer than five customers will arrive in a 20 minute segment? The probability is . (Round to four decimal places as needed.)

Kindly answer in excel sheet

Answer 1

(I am providing the EXCEL commands for this question.)
Here, X = arrivals to a bank ATM. Here, $\lambda$ = 6 per 10 minutes = mean. Now, X ~ Poisson($\lambda$ = 6).

(a) The probability that in a given 10 minute segment, three customers will arrive at the ATM = 0.0892.
EXCEL command: =POISSON(3,6,0).

(b) Here, $\lambda$ = 12 per 20 minutes = mean. Now, X ~ Poisson($\lambda$ = 12). The probability that fewer than five customers will arrive in a 20 minute segment = 0.0076.
EXCEL command: =POISSON(4,12,1).