A wooden kitchen cabinet is carefully inspected at the manufacturing facility before it is sent to a retailer. The random variable X is the number of defects found in a randomly selected cabinet. The probability distribution for X is given in the table below.
An automobile insurance policy depends on many factors, including the vehicle type, year, make, and model, type of coverage, your driving history, your insurance score based on claims history, payment history, and credit score, and your state of residence.4 Suppose that for some driver category, the probability distribution for the random variable Y, the amount (in dollars) paid to policyholders for claims in one year, is given in the table below.
Camden, New Jersey, has one of the highest crime rates in the United States. As a result, a new Camden County Police Department will include 400 officers and be responsible for an area covering nine square miles.5 Suppose the number of times a police cruiser from this new department drives through the Whitman Park neighborhood during a one-hour period is a random variable X, with probability distribution as given in the table below.
Suppose a one-hour period is randomly selected.
a. What is the probability that no police cruiser will drive through the neighborhood?
b. What is the probability that at least one police cruiser will drive through the neighborhood?
c. What is the probability that at most two police cruisers will drive through the neighborhood?
d. What is the probability that more than seven police cruisers will drive through the neighborhood?
e. Suppose at least two police cruisers were sighted in the neighborhood during the one-hour period. What is the probability that there were at least four during this time?