TOMRA Systems ASA is a Norwegian company that manufactures reverse vending machines (RVMs). In most cases, RVMs are used in markets that have deposits on beverage containers, offering an efficient and convenient method of identifying the deposit amount of each container returned and providing a refund to the customer. Prices for such machines range from about $9,000 for single-container machines to about $35,000 for higher-volume, multi-container (can, plastic, glass) machines. For a single-container machine to pay for itself in one year, it would need to generate an average monthly income of more than $750. The following sample of single-machine monthly incomes was obtained to determine if that goal could be reached:

This sample is contained in the file labeled RVMIncome.
a. Conduct a hypothesis test to determine if the goal can be reached. Use a significance level of 0.05 and the p -value approach.
b. There are 10 sites in which an RVM could be placed. Unknown to the vendor, only four of the sites will allow the vendor to meet the goal of paying for the machine in one year. If he installs four of the RVMs, determine the probability that at least two of them will be paid off in a year.