Acar insurance company has 2, 500 policy holders. the expected claim paid to a policy holder during a year is $1,000 with a standard deviation of $900. what premium should the company charge each policy holder to assure that with probability 0.999, the premium income will cover the cost of the claims? compute the answer both with chebyshev's inequality and with the clt.

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.