Question

In: Statistics and Probability

An insurance company reports the following distribution of the claim sizes for an auto insurance policy...

An insurance company reports the following distribution of the claim sizes for an auto insurance policy from a sample of 87 cases.

Claim Size (in $) Number of claims

2000 to 3000    15

3000 to 4000 10

4000 to 5000    20

5000 to 6000 15

6000 to 7000 10

7000 to 8000    10

8000 to 9000    7

( a ) Construct a histogram for the data.

( b ) a frequency polygon for the data.

( c the mean and the standard deviation of the claim size.

( d ) the percentage of claims whose claim size is less than $7000.

( e ) the percentage of claims whose claim size is at least $5000.

( f ) the percentage of claims whose claim size is $8000 or above.

Solutions

Expert Solution


Related Solutions

An insurance company sells an insurance policy for $1000. If there is no claim on a...
An insurance company sells an insurance policy for $1000. If there is no claim on a policy, the company makes a profit of $1000. If there is a claim on a policy, theȱȱcompany faces a large loss onȱȱthat policy. The expected value to the company, per policy, is $250. Which of the following statements is (are) true? A: The most likely outcome on any single policy is a profit for the company of $250. B: If the company sells only...
Auto insurance premiums. Suppose a newspaper article states that the distribution of auto insurance premiums for...
Auto insurance premiums. Suppose a newspaper article states that the distribution of auto insurance premiums for residents of California is approximately normal with a mean of 1504. The article also states that 15% of California residents pay more than 1940. 1. What is the Z score that corresponds to the top 15% (or the 85thth percentile) of the standard normal distribution? Round your answer to 4 decimal places. 2. What is the mean insurance cost? 3. What is the cutoff...
The navy reports that the distribution of waist sizes among male sailors is approximately normal, with...
The navy reports that the distribution of waist sizes among male sailors is approximately normal, with a mean of 32.6 inches and a standard deviation of 1.3 inches Part A: A male sailor whose waist is 34.1 inches at what percentile? Mathematically explain your reasoning and justify your work mathematically Part B: The navy uniform supplier regularly stocks uniform pants between sizes 30 and 36. Anyone with a wasut circumference outisde that interval requires a customized order. Describe what this...
Define insurance and discuss the principle of indemnity. In an auto insurance policy, explain the meaning...
Define insurance and discuss the principle of indemnity. In an auto insurance policy, explain the meaning of the numbers 100/300/75. Explain what a living will is and how it differs from a health care proxy.
An automobile insurance company predicts that 15% of policy holders file a claim within the next...
An automobile insurance company predicts that 15% of policy holders file a claim within the next year. Since this company has many policy holders, we may assume that filing a claim is independent between policy holders. a. If 15 policy holders are randomly selected, what is the probability that exactly two will file a claim within the next year? What calculator command and inputs did you use? b. If 15 policy holders are randomly selected, what is the probability that...
An automobile insurance company predicts that 15% of policy holders file a claim within the next...
An automobile insurance company predicts that 15% of policy holders file a claim within the next (8pt) year. Since this company has many policy holders, we may assume that filing a claim is independent between policy holders. a. If 15 policy holders are randomly selected, what is the probability that exactly two will file a claim within the next year? What calculator command and inputs did you use?
Tedy Brown has an accounts receivable insurance policy that allows the company to claim for bad...
Tedy Brown has an accounts receivable insurance policy that allows the company to claim for bad debts of up to $50 000 per annum. The amount covered under the policy has remained the same since 2012 (when the accounts receivable balance averaged $2 000 000). Since 2012, the average accounts receivable balance has increased to $3 800 000. Issue 2 Tedy Brown sales representatives are entitled to commission on sales above quarterly targets. Any commission earned is required to be...
An automobile insurance company predicts that 15% of policy holders file a claim within the next...
An automobile insurance company predicts that 15% of policy holders file a claim within the next (8pt) year. Since this company has many policy holders, we may assume that filing a claim is independent between policy holders. a. If 15 policy holders are randomly selected, what is the probability that exactly two will file a claim within the next year? What calculator command and inputs did you use? b. If 15 policy holders are randomly selected, what is the probability...
An insurance company has the following profitability analysis of its services: Life Insurance Auto Insurance Home...
An insurance company has the following profitability analysis of its services: Life Insurance Auto Insurance Home Insurance Revenues $5,000,000 $10,000,000 $3,000,000 Commissions (1,000,000) (2,000,000) (600,000) Payments (3,000,000) (7,300,000) (2,000,000) Fixed Costs (500,000) (500,000) (500,000) Profit $ 500,000 $ 200,000 ($ 100,000) The fixed costs are distributed equally among the services and are not avoidable if one of the services is dropped. What is the profitability of the remaining services if all services with losses are dropped?
Although domiciled in Nebraska, Auto Insurance Company is licensed to sell auto insurance in 10 states....
Although domiciled in Nebraska, Auto Insurance Company is licensed to sell auto insurance in 10 states. A different set of rates applies in each state. In five states, prior approval of rates is required. Two states have a file-and-use law, and the remaining three states have a flex-rating law. Auto Insurance Company has experienced poor underwriting results and needs to increase its rates. Explain how each of the above rating laws would apply to Auto Insurance Company. Describe some possible...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT