The number of annual claims per policy at a health insurance company has a norma
ID: 3357859 • Letter: T
Question
The number of annual claims per policy at a health insurance company has a normal distribution with mean $1200 and standard deviation $250. Patrick has a health insurance policy with the company, which has an annual deductible of $700. This means that if Patrick’s claims in one year are less than $700, then he pays the bill and the company pays nothing, but if his claims are over $700, then he pays $700 and the company pays the rest. What is the probability that the company will not pay anything net year against Patrick’s policy?
Explanation / Answer
The company will not pay anything if Patrick's claims are less than or equal to $700.
Mean = 1200 = 250
=> P(x <= 700)
= P(z <= ((700 - 1200) / 250))
= P(z <= -2)
= 0.0228.