An auto insurance company has 32,000 clients, and 5% of their clients submitted a claim in the past year. We will take a sample 3,200 clients, and determine how many of them have submitted a claim in the past year.
a) What is the sampling distribution for the sample proportion?
b) Increased road accidents have caused an increase in these claims. What is the probability that the proportion of claims in the sample is more than 9%?
An auto insurance company has 32,000 clients, and 5% of their clients submitted a claim in...
4. Insurance companies charge clients under 25 more for auto insurance than clients over 25. They claim this is because clients under 25 have more accidents. A random sample of 40 drivers under 25 had a mean of 1.2 accidents per year with a standard deviation of .1. A sample of 40 drivers over 25 had a mean of .94 accidents per year with a standard deviation of .2. From this data can we conclude the Insurance companies are correct...
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0016. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0016. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis...
State Farm Insurance studies show that in Colorado, 55% of the auto insurance claims submitted for property damage are submitted by males under 25 years of age. Suppose 10 property damage claims involving automobiles are selected at random. (a) Let r be the number of claims made by males under age 25. Make a histogram for the r-distribution probabilities. (b) What is the probability that six or more claims are made by the males under age 25? (c) What is...
State Farm Insurance studies show that in Colorado, 45% of the
auto insurance claims submitted for property damage were submitted
by males under 25 years of age. Suppose 12 property damage claims
involving automobiles are selected at random.
(a) Let r be the number of claims made by males under
age 25. Make a histogram for the r-distribution
probabilities.
(b) What is the probability that three or more claims are made by
males under age 25? (Use 3 decimal places.)...
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a variance of 0.0025. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H, and the alternative hypothesis...
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a standard deviation of 0.05. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.05. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H, and the...
#6. A car insurance company has high-risk, medium-risk, and low-risk clients, who have, respectively, probabilities.04,.02, and.01 of filing claims within a given year. The proportions of the numbers of clients in the three categories are .15, .25, and.60, respectively (a) What is the probability that a random client doesn't file a claim? (b) What proportion of the claims filed each year come from high-risk clients? (c) What is the probability that a random client who didn't file a claim is...
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A company makes auto batteries. They claim that 81% of their LL70 batteries are good for 70 months or longer. Assume that this claim is true. Let p be the proportion in a random sample of 70 such batteries that are good for 70 months or more. a. What is the probability that this sample proportion is within 0.02 of the population proportion? Round your answer to two decimal places b. What is the probability that this...
AICUS (Auto Insurance Company of the United States) paid out $62,750,000 in car insurance claims last year. During that year, the company had 100,000 clients and charged each client $600 for insurance. Nine hundred and ninety-nine thousand, five hundred of its clients did not get into any accidents. We will call this the low-risk group. Two-hundred-and-fifty clients had minor accidents that cost $1,000 each. Call this the moderate-risk group. An additional 250 clients had major accidents involving lawsuits that cost...
Anystate Auto Insurance Company has shown that their paid claims have a standard deviation that is approximately $260. We would like to take a sample of their paid claims such that our estimate has a margin of error within $50 of the true mean. What sample size would we need to take if we wanted to use a 99% confidence level? Confidence Level = Standard Deviation = Width = Sample Size =