Question

The Mountain State Office of State Farm Insurance Company reports that approximately 90% of all automobile damage liability claims are made by people under 25 years of age. A random sample of size five automobile insurance liability claims are selected, what is the probability that in that sample, at most 4 automobile damage liability claims are made by people under 25 years of age?

Answer 1

Let the random variable, X = number of automobile damage liability claims are made by people under 25 years of age

When we want to calculate the probability of the number of success in a fixed number of trails (Bernoulli's trials i.e. two possible outcomes, success/failure), the binomial distribution follows.

Hence the sample size of 5 claims will have a binomial distribution with parameters n and p.

n = number of claims = 5

p = probability of success = 0.80

The required probability is,

The probability mass function for the binomial distribution is defined as,

hence,