An insurance company estimates that it should make an annual

An insurance company estimates that it should make an annual profit of $150 on each homewoner\'s policy written, with a standard deviation of $6900. if it writes 13225 if these policies, what is the probability that the company will be profitable? assume that policies are independent of each other and that the company\'s total profit follows normal model.

Solution

let X be a random variable denoting profits of normal distribution with mean 150 and sd 6900

now to find P(X>0),

after computing we get P(X>0)=0.500001

hence in 13225 policies the profit probability is (0.500001)¹³²²⁵