(a) To find the value of z corresponding to a cumulative area equal to 0.7486.

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Answer 1

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.3, Problem 7.24E

To determine

(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

To determine

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

To determine

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

To determine

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.

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Questions An insurance company's cumulative incurred claims for the last 5 accident years are given in the following table: Development Year Accident Year 0 2018 1 2 3 4 245 267 274 289 292 2019 255 276 288 294 2020 265 283 292 2021 263 278 2022 271 It can be assumed that claims are fully run off after 4 years. The premiums received for each year are: Accident Year Premium 2018 306 2019 312 2020 318 2021 326 2022 330 You do not need to make any allowance for inflation. 1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method. (b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method. 2. Comment on the differences in the reserves produced by the methods in Part 1.

Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. Then calculate it again, letting Row 2 represent the x-values and Row 1 the y-values. What effect does switching the variables have on r? Row 1 Row 2 13 149 25 36 41 60 62 78 S 205 122 195 173 133 197 24 Calculate the correlation coefficient r, letting Row 1 represent the x-values and Row 2 the y-values. r=0.164 (Round to three decimal places as needed.) S 24

Answer 2

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.3, Problem 7.24E

To determine

(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

To determine

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

To determine

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

To determine

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.3, Problem 7.24E

To determine

(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

To determine

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

To determine

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

To determine

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.3, Problem 7.24E

To determine

(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

To determine

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

To determine

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

To determine

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 7.3, Problem 7.24E

To determine

(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

To determine

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

To determine

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

To determine

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.

Answer 6

Chapter 7.3, Problem 7.24E

To determine

(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

Answer 7

Chapter 7.3, Problem 7.24E

To determine

(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

Answer 8

To determine

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

Answer 9

To determine

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

Answer 10

To determine

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

Answer 11

To determine

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

Answer 12

To determine

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.

Answer 13

To determine

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

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(a) To find the value of z corresponding to a cumulative area equal to 0.7486.

Solution Summary: The author explains how to find the value of z corresponding to a cumulative area equal to 0.7486.

Concept explainers

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(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.

Want to see the full answer?

Chapter 7 Solutions

(a) To find the value of z corresponding to a cumulative area equal to 0.7486.

Solution Summary: The author explains how to find the value of z corresponding to a cumulative area equal to 0.7486.

Concept explainers

Videos

(a) To find the value of z corresponding to a cumulative area equal to 0.7486.

(b) To find the value of z corresponding to a cumulative area equal to 0.0735.

(c) To find the value of z where the area between zand the positive infinity is 0.3508.

(d) To find the value of z where the area between z and the positive infinity is 0.0212.

Want to see the full answer?

Chapter 7 Solutions

(a)

To find the value of z corresponding to a cumulative area equal to 0.7486.

(b)

To find the value of z corresponding to a cumulative area equal to 0.0735.

(c)

To find the value of z where the area between zand the positive infinity is 0.3508.

(d)

To find the value of z where the area between z and the positive infinity is 0.0212.