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Directions: Print this test out, then answer all questions. Show work on the provided answer pages. If you use calculator functions or JMP functions, you may wish to show those as well. Partial credit may be given. Remember, this test must be submitted as a PDF document in the Assignments Link under the Learning Technologies menu. Only the answers need to be submitted to me, and not the test questions. 1. An automobile insurer studied the number of claims filed by their policyholders in a given year. The results are as follows: Number of claims (X) 0 1 2 3 4 P(X) .76 .12 .07 .04 .01 a. There are two properties that tell you this is a discrete probability distribution. What are they? b. What is the probability that a randomly selected policyholder files three claims? c. What is the probability that a randomly selected policyholder files more than one claim? d. What is the probability that a randomly selected policyholder files at most two claims? e. What is the mean & standard deviation number of claims filed by a policyholder? 2. An insurance company has 20 policyholders who are considered to be high risk. The probability that one of these clients will file a major claim in the next year is 0.2. Assuming a binomial distribution, a. What is the probability that exactly 3 of them will file a major claim in the next year? b. What is the probability that at most 4 will make a major claim in the next year? c. What is the probability that at least 7 of them will file a claim in the next year? d. What are the mean, variance & standard deviation of the number of claims that will be filed next year? 3. A telemarketer makes random phone calls at a call center to try and generate interest on a particular product. The probability of getting a "call-back" on any given call is known to be 6%. Assuming a geometric/negative binomial distribution, what is the probability: a. the telemarketer gets his first call-back on his 8th try? b. the telemarketer has 8 no call-backs before his first call-back? c. the telemarketer gets his third call-back on his 10th try? d. The telemarketer gets 14 no call-backs before he gets his 4th callback? In addition, e. Find the mean number of non call-backs before his 5th call-back. 4. A small life insurance company has determined that on the average it receives 10 death claims per day. Assuming a Poisson distribution, a. Find the probability that the company receives 11 death claims on a randomly selected day. b. Find the probability that the company receives at most 9 death claims on a randomly selected day. c. Find the probability that the company receives at least 12 death claims on a randomly selected day. d. Find the probability that the company receives 55 death claims on a randomly selected 5-day work week.

Directions: Print this test out, then answer all questions. Show work on the provided answer pages. If you use calculator functions or JMP functions, you may wish to show those as well. Partial credit may be given. Remember, this test must be submitted as a PDF document in the Assignments Link under the Learning Technologies menu. Only the answers need to be submitted to me, and not the test questions.

1. An automobile insurer studied the number of claims filed by their policyholders in a given year. The results are as follows:

Number of claims (X) 0 1 2 3 4
P(X) .76 .12 .07 .04 .01

a. There are two properties that tell you this is a discrete probability distribution. What are they?
b. What is the probability that a randomly selected policyholder files three claims?
c. What is the probability that a randomly selected policyholder files more than one claim?
d. What is the probability that a randomly selected policyholder files at most two claims?
e. What is the mean & standard deviation number of claims filed by a policyholder?

2. An insurance company has 20 policyholders who are considered to be high risk. The probability that one of these clients will file a major claim in the next year is 0.2. Assuming a binomial distribution,
a. What is the probability that exactly 3 of them will file a major claim in the next year?
b. What is the probability that at most 4 will make a major claim in the next year?
c. What is the probability that at least 7 of them will file a claim in the next year?
d. What are the mean, variance & standard deviation of the number of claims that will be filed next year?

3. A telemarketer makes random phone calls at a call center to try and generate interest on a particular product. The probability of getting a "call-back" on any given call is known to be 6%. Assuming a geometric/negative binomial distribution, what is the probability:
a. the telemarketer gets his first call-back on his 8th try?
b. the telemarketer has 8 no call-backs before his first call-back?
c. the telemarketer gets his third call-back on his 10th try?
d. The telemarketer gets 14 no call-backs before he gets his 4th callback?
In addition,
e. Find the mean number of non call-backs before his 5th call-back.

4. A small life insurance company has determined that on the average it receives 10 death claims per day. Assuming a Poisson distribution,
a. Find the probability that the company receives 11 death claims on a randomly selected day.
b. Find the probability that the company receives at most 9 death claims on a randomly selected day.
c. Find the probability that the company receives at least 12 death claims on a randomly selected day.
d. Find the probability that the company receives 55 death claims on a randomly selected 5-day work week.

Directions: Print this test out, then answer all questions. Show work on the provided answer pages. If you use calculator functions or JMP functions, you may wish to show those as well. Partial credit may be given. Remember, this test must be submitted as a PDF document in the Assignments Link under the Learning Technologies menu. Only the answers need to be submitted to me, and not the test questions.

1. An automobile insurer studied the number of claims filed by their policyholders in a given year. The results are as follows:

Number of claims (X) 0 1 2 3 4
P(X) .76 .12 .07 .04 .01

a. There are two properties that tell you this is a discrete probability distribution. What are they?
b. What is the probability that a randomly selected policyholder files three claims?
c. What is the probability that a randomly selected policyholder files more than one claim?
d. What is the probability that a randomly selected policyholder files at most two claims?
e. What is the mean standard deviation number of claims filed by a policyholder?

2. An insurance company has 20 policyholders who are considered to be high risk. The probability that one of these clients will file a major claim in the next year is 0.2. Assuming a binomial distribution,
a. What is the probability that exactly 3 of them will file a major claim in the next year?
b. What is the probability that at most 4 will make a major claim in the next year?
c. What is the probability that at least 7 of them will file a claim in the next year?
d. What are the mean, variance standard deviation of the number of claims that will be filed next year?

3. A telemarketer makes random phone calls at a call center to try and generate interest on a particular product. The probability of getting a "call-back" on any given call is known to be 6%. Assuming a geometric/negative binomial distribution, what is the probability:
a. the telemarketer gets his first call-back on his 8th try?
b. the telemarketer has 8 no call-backs before his first call-back?
c. the telemarketer gets his third call-back on his 10th try?
d. The telemarketer gets 14 no call-backs before he gets his 4th callback?
In addition,
e. Find the mean number of non call-backs before his 5th call-back.

4. A small life insurance company has determined that on the average it receives 10 death claims per day. Assuming a Poisson distribution,
a. Find the probability that the company receives 11 death claims on a randomly selected day.
b. Find the probability that the company receives at most 9 death claims on a randomly selected day.
c. Find the probability that the company receives at least 12 death claims on a randomly selected day.
d. Find the probability that the company receives 55 death claims on a randomly selected 5-day work week.

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