An auditor for Health Maintenance Services of Georgia...

An auditor for Health Maintenance Services of Georgia reports 40 percent of the policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company records. a. How many of the policyholders would you expect to have filed a claim within the last year? b. What is the probability that ten of the selected policyholders submitted a claim last year? c. What is the probability that ten or more of the selected policyholders submitted a claim last year? d. What is the probability that more than ten of the selected policyholders submitted a claim last year?

An auditor for Health Maintenance Services of Georgia reports 40 percent of the policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company records.
a. How many of the policyholders would you expect to have filed a claim within the last year?
b. What is the probability that ten of the selected policyholders submitted a claim last year?
c. What is the probability that ten or more of the selected policyholders submitted a claim last year?
d. What is the probability that more than ten of the selected policyholders submitted a claim last year?

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Key Concepts

Binomial Probability Calculation

This involves using the probability mass function (PMF) of the binomial distribution, which gives the probability of exactly k successes in n trials. The formula is given by C(n, k) * p^k * (1-p)^(n-k), where C(n, k) represents the binomial coefficient, calculating the number of ways to choose k successes from n trials.

Cumulative Probability

Cumulative probability in a binomial context is the sum of probabilities for a range of outcomes. It is used to find the probability that the random variable is greater than, less than, or between certain values, often involving summing the probability mass function over the desired range of values.

Binomial Distribution

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, each with the same probability of success. It is characterized by two parameters: the number of trials (n) and the probability of success (p) in each trial.

Expected Value

In the context of a binomial random variable, the expected value is the average number of successes one would anticipate over many repetitions of the experiment and is calculated using the formula np, where n is the number of trials and p is the probability of success in each trial.

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