Question

7. A coffee shop serves an average of 75 customers per hour during the morning rush.
a. Which distribution we have studied is most appropriate for calculating the probability of a given
number of customers arriving within one hour during this time of day?
b. What are the mean and the standard deviation of the number of customers this coffee shop serves
in one hour during this time of day?
c. Would it be considered unusually low if only 60 customers showed up to this coffee shop in one
hour during this time of day?
d. Calculate the probability that this coffee shop serves 70 customers in one hour during this time of
day.

Answer 1

a)The Poisson distribution

b)The Poisson has its mean equal to its variance = λ so a mean of 75 customers and a standard deviation of 75−−√≈8.66 customers.

c)Yes. Exactly 60 would be rare, and even at most 60 is uncommon. As the Poisson is a counting distribution, to calculate 60 or fewer events, the cumulative distribution needs to be built up manually.

d) The probability that this coffee shop serves 70 customers in one hour during this time of

day is:

P(X=70λ=75)

=((75^70)(e^−75))/70!

=exp(70ln(75)−75−lnΓ(71))

≈exp(302.2242−75−230.439)

≈e^−3.214876

≈0.04016033