Final answer:
To determine the probability of a single value exceeding $963, use the normal distribution. For sample means, use the central limit theorem. Adverse selection in insurance arises due to asymmetric information between the company and policyholders.
Step-by-step explanation:
Finding Probability in Different Scenarios
To find the probability that a single randomly selected value exceeds $963, one must use the normal distribution with the given mean and standard deviation. For the average of a sample of 68 policies, the calculation would use the sampling distribution of the sample mean, which has a lower standard deviation thanks to the central limit theorem.
For the comparison of auto insurance costs between teenage boys and girls, a hypothesis test using the sample means, population standard deviations, and corresponding sample sizes will help infer if there is a significant difference in the means.
In the example concerning automobile insurance costs, totaling the costs for the three groups of drivers shows how insurance companies calculate risks and premiums to stay profitable. However, the issue of adverse selection arises when there's asymmetric information, leading high-risk drivers to be more likely to purchase insurance, potentially causing losses for the insurance company.