An insurance agency is reviewing its sale of automobile insurance policies''

  An insurance agency is reviewing its sale of automobile insurance policies for the coming year. Using historical data the agency determines losses on each policy have a mean of $1000 and a standard deviation of $200. If the insurance agency sells 100 such policies at the premium of $1050 each, what is the probability the insurance agency loses money selling the policies? (Hint - Let 𝑋𝑖 denote the loss on the 𝑖th policy, 𝑖 = 1, … , 100. The average loss on the policies is 𝑋̅. What average loss causes the agency to lose money?)