Question

An insurance company has 10,000 automobile policyholders. The expected yearly claim per policyholder is $240, with a standard deviation of $800. Approximate the probability that the total yearly claim exceeds $2.7 million.

Answer 1

Answer:

almost 0%

Step-by-step explanation:

Given that for an insurance company with 10000 automobile policy holders, the expected yearly claim per policyholder is $240 with a standard deaviation of 800

using normal approximation, the probability that the total yearly claim exceeds $2.7 million is calculated as follows:

Sea sumatoria de x = SUMX, tenemos que:

$P (SUMX \geq 2700000) = P(\frac{SUMX - 240*10000}{800 *\sqrt{10000} } \geq \frac{2700000 - 240*10000}{800 *\sqrt{10000} })$

$= P (z\geq \frac{2700000 - 240*10000}{800 *\sqrt{10000}})$

= P (z => 3.75)

= 1 - P ( z < 3.75)

P = 1 - 0.999912

P = 0.000088

Which means that the probability is almost 0%