If an insurance company has 10000 policies, and each has 0.1 probability of making a claim, what is the standard deviation of the fraction of policies which result in a claim?

Answer: S. D = + / - 0.003

The standard deviation of the fraction of policies which result in a claim is + / - 0.003

Step-by-step explanation:

Given;

Probability of making a claim p = 0.1

Number of company policies n = 10000

Standard deviation is the measure of how spread out numbers are.

S. D = √ (p (1-p) / n)

Where,

p = 0.1

n = 10000

S. D = √ (0.1 (1-0.1) / 10000)

S. D = √ (0.1*0.9/10000)

S. D = √ (0.000009)

S. D = + / - 0.003

0.003

Step-by-step explanation:

Since each of the policy have the same chance of success, then it follows a binomial distribution (only two outcome; success or failure).

α = √ (p (1-p) / n) = √ (0.1 (1-0.1) / 10000) = √ 0.000009 = 0.003

where p = 0.1, α = standard deviation.