1. An average of 6.3 cases of graffiti vandalism occur per week in a large city. Write your answer up to 4 decimal places.

(a) What is the probability that there are exactly 2 cases of graffiti vandalism in this city during any given week?

(b) Find the probability that during any given day, between 2 to 4 cases inclusive of graffiti vandalism will occur in this city.

(c) Find the mean and standard deviation of cases of graffiti vandalism in this city during any given day.

2. A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 3%. The inspector of the retailer picks a random sample of 77 items from a shipment. Write your answer up to 4 decimal places.

(a) Compute the probability that exactly 3 devices are defective.

(b) Find the probability that at most 22 devices are defective.

(c) Find the mean and standard deviation of the number of defective devices.

3. Suppose that 60% of all customers of a large cable company subscribe to Internet service, 40% subscribe to phone service, and 25% have both types of services. If a customer is selected at random, what is the probability that the customer.

(a) has either internet service or phone service?

(b) has neither of these services?

(c) has exactly one of these two services?