Question

In: Statistics and Probability

Accidents records by an auto insurance company suggest that theprobability that an insured driver has...

Accidents records by an auto insurance company suggest that the probability that an insured driver has an accident is 0.15.If an accident occurs, the damage to the vehicle amounts to an average of 5380.What premium should the insurance company charge, in order to have an expected profit of 2500?

a)On average the insurer should charge _? (round to 2 decimal points.?

Solutions

Expert Solution

premium = probability(accident) * payment(accident) + expected profit

given,

P(accident) = 0.15

payment (accident) = $5380

expected profit = $2500

a.

premium that company should charge :

premium = probability(accident) * payment(accident) + expected profit

= 0.15 * $5380 + $2500

= $ 3307

premium = $ 3307


Related Solutions

Accidents records by an auto insurance company suggest that the probability that an insured driver has...
Accidents records by an auto insurance company suggest that the probability that an insured driver has an accident is 0.05 If an accident​ occurs, the damage to the vehicle amounts to an average of ​$6240. What premium should the insurance company​ charge, in order to have an expected profit of ​$1000? On average the insurer should charge ​$.... ​(Round to 2 decimal​ points.)
A random sample of eight auto drivers insured with a company and having similar auto insurance...
A random sample of eight auto drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experience (in years) and the monthly auto insurance premium (in dollars). Driving Experience(years) 5 2 12 9 15 6 25 16 Monthly Premium(dollars) 64 87 50 71 44 56 42 60 Answer the following questions. Predict the average monthly auto insurance premium for drivers with 10 years of driving experience and provide the 95% confidence...
A random sample of eight auto drivers insured with a company and having similar auto insurance...
A random sample of eight auto drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experience (in years) and the monthly auto insurance premium (in dollars). Driving Experience(years) 5 2 12 9 15 6 25 16 Monthly Premium(dollars) 64 87 50 71 44 56 42 60 Answer the following questions. (a) Does the insurance premium depend on driving experience or does the driving experience depend on insurance premium? Do you...
An insurance company is interested in estimating the percentage of auto accidents that involve teenage drivers....
An insurance company is interested in estimating the percentage of auto accidents that involve teenage drivers. Suppose the percentage of auto accidents that involved teenage drivers last year was 15%. The company wants to know if the percentage has changed this year. They check the records of 600 accidents selected at random from this year and note that teenagers were at the wheel in 60 of them. (a) Create a 90% confidence interval for the percentage of all auto accidents...
The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one...
The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is .15. a) Show the sampling distribution of p if a random sample of 150 insured individuals is used to estimate the proportion having received at least one ticket. b) What is the probability that the sample proportion will be within +-.03 of the population proportion?
A random sample of 8 drivers insured with a company and having similar auto insurance policies...
A random sample of 8 drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums: Driving Experience (years) Monthly Auto Insurance Premium 5 $64 2 $87 12 $50 9 $71 15 $44 6 $56 25 $42 16 $60 a. Make a scatter plot of the data b. Calculate the correlation coefficient c. Calculate a simple linear regression with Premium as the dependent variable...
A random sample of eight drivers insured with a company and having similar auto insurance policies...
A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums. Driving Experience (years) Monthly Auto Insurance Premium $ 5 64 2 87 12 50 9 71 15 44 6 56 25 42 16 60 a. Does the insurance premium depend on the driving experience or does the driving experience depend on the insurance premium? Do you expect a...
An insurance company checks police records of 500 accidents and finds that teenagers were at the...
An insurance company checks police records of 500 accidents and finds that teenagers were at the wheels in 87 accidents. Assume that the true population proportion of accidents with teen-agers at the wheels is : p = 0.20.   Estimate the probability that the sample proportion of teen age drivers in this population is no more than the observed proportion of auto accidents that involve teenagers. Use the simulated data on phat ( "phat.rda") from 5000 simulations under the null hypothesis:...
An insurance company checks police records of 549 accidents and finds that teenagers were at the...
An insurance company checks police records of 549 accidents and finds that teenagers were at the wheels in 87 accidents. At a confidence level of 92%, calculate the margin of error in the estimated proportion of all auto accidents that involve teenagers. four decimals.
Driver error can be listed as the cause of approximately 54% of all fatal auto accidents,...
Driver error can be listed as the cause of approximately 54% of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. Using α = 0.05, is the AAA proportion accurate?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT