Question: Question 4

A customs official has determined that about thirty percent of citizens returning from abroad have goods they do not declare. She has selected fifteen returning citizens at random.

What is the expected number of citizens in the sample with undeclared goods? What is the standard deviation?

a) What is the probability that at least three of the fifteen have undeclared goods?

b) What is the probability that more than the expected number have undeclared goods?

c) An extensive campaign to decrease smuggling could reduce the fraction of those not declaring goods to 5%. Estimate the probability that at least three of 25 randomly-selected returning citizens would have undeclared goods after such a campaign.