The average number of customers served by The Copy Shop during a typical morning (9am to noon) is 12. One morning, The Copy Shop has to close for 15 minutes.
What is the probability that no customers will arrive during this 15 minute period?
X = number of customers
a. X ~ binomial
b. X ~ negative binomial
c. X ~ hypergeometric
d. X ~ Poisson

d, p = 0.4493

Step-by-step explanation: this question is solved using a possion probability distribution because the event is occurring at a fixed rate.

For this question of ours the fixed rate is the fact that 12 customers visiting the shop within 15 minutes.

For this question our fixed rate (u) = 12/15 = 0.8

The probability distribution for possion is given as

P(x=r) = (e^-u * u^r) / r!

At this point x = 0 ( no customers coming to the shop)

P(x=0) =( e^-0.8 * 0.8^0)/ 0!

P(x=0) = (e^-0.8 * 1)/1

P(x=0) = e^-0.8

P(x=0) = 0.4493

answer: -8.2562234e+13