Question

3. Consider the Atlanta airport, which sees 300,000 passengers per day. Approximately 1 in 100,000 customers per day forget their ID and cannot board their flights.

a. Consider a 7-day week. What is the expected number of customers who forget their ID in a 7-day week?

b. What is the standard deviation of the number of customers who forget their ID in a 7-day week?

c. What is the probability that no customers forget their ID in a 7-day week?

d. What is the probability that no customers forget their ID in a single day?

e. Consider a 7-day week. What is the probability that the number of customers who forget their ID in a 7-day week is less than the mean plus the standard deviation?

5. In a particular university, the number of claims of academic integrity violation per semester for one particular department is distributed as a Poisson random variable. Assume the probability of exactly one claim being filed is represented by the unknown value a and the probability of exactly zero claims being filed is represented by the unknown value 4a. What is the expected number of claims being filed per semester?

Answer 1

Multiple sub-parts. Solving first four

3.

a) expected number of customers who forget their ID in a 7-day week = 1*3*7 = 21

b) standard deviation for proportion,s =

p = 1/100000 = 0.00001

n = 300000*7 = 2100000

So, s =

= 0.00000218

c) probability that no customers forget their ID in a 7-day week = (Probability of not forgetting for single customer)^(total customers in 7 days)

= (1-0.00001)^2100000 = 0.00000000076

d) probability that no customers forget their ID in a single day = (1-0.00001)^300000 = 0.05