Ch 2: Probability Distributions for Analyzing Risk

In analyzing Patridge's three year loss data for forecasting purposes, what is the mean loss value?

$2,472

If 95.44 percent of all outcomes are within two standard deviations above and below the mean and 2.15 percent of all outcomes are between two and three standard deviations above and 2.15 percent of all outcomes are between two and three standard below the mean, the percentage of all outcomes that lie outside three standard deviations above or below the mean is Choose one answer. A. .13 B. .26 C. 2.15 D. 4.30

.26

In flipping a coin, each of the two possible outcomes, heads or tails, has an equal probability of 50%. Because on a particular flip of a coin, only one outcome is possible, these outcomes are

Mutually exclusive

Which one of the following describes how probabilities are expressed?

Numerically, as a fraction, a percentage, or a decimal.

Which one of the following statements is correct with respect to continuous probability distributions?

One way of presenting a continuous probability distribution is to divide the distribution into a countable number of bins

In a normal distribution, fewer than 5% of outcomes are

Outside two standard deviations above or below the mean

Which one of the following statements is true regarding the nature of probability?

Probabilities deduced solely from historical data may change as new data are discovered or the environment changes.

One difference between theoretical probability distributions and empirical probability distributions is that for empirical probability distributions the

Probabilities may change as new data are discovered.

Hank has determined the expected number of workers comp claims in a given year. Hank next calculates the standard deviation of potential outcomes. Calculating the standard deviation

Provides a measure of how sure Hank can be in his estimate of claims.

This graph illustrates a probability distribution. Which one of the following statements is true regarding the information presented in this graph?

The most frequently occurring value is seven

One of the ways in which probabilities can be developed is theoretically. Which one of the following is an example of an event for which probability can be determined theoretically?

The number of times heads can be expected to turn up over multiple coin tosses

A chart showing the probability of obtaining the numbers one through six on one roll of one die represents a

Theoretical probability distribution

Which one of the following statements is correct with respect to empirical probability distributions?

They provide a mutually expensive, collectively exhaustive list of outcomes

The sum of probabilities in a probability distribution must be

1.00

An organization's premises and operations liability losses have a severity distribution with a mean of $10,000 and a standard deviation of $15,000. What is the coefficient of variation for this distribution?

1.5

The theoretical probability of a head on a coin toss is 50%. Based on the law of large numbers, which one of the following is the number of coin tosses most likely to result in an empirical frequency of 50% receiving a head on a coin toss?

100

The number of auto physical damage claims for fleet vehicles at Right-a-Way Delivery Service in any year is normally distributed. Based on this info what is the probability that between 737 and 762 auto physical damage claims will occur next year?

13.6%

Granton Manufacturing uses diamond-point cutting tools to manufacture metal plates. The diamond points have an average life of 90 days. Some points last longer and others wear out more quickly; however, overall the average life of the diamond points follows a normal distribution curve with each standard deviation equaling 10 days. Replacing a point requires only 15 minutes. However, if a point fails, Granton often must scrap some of the metal plates, and the process to return to full operations takes over two hours. What percentage of diamond points are likely to wear out before 80 days? A. 0.13% B. 2.15% C. 15.87% D. 34.14%

2.28%

If in calculating the mean, the outcomes are 2,2,5,5, and 6, the mean is

4

The property damage claims experienced by Runyon Company are normally distributed. The mean of the distribution of property claims is $620 and the coefficient of variation is .75. What is the standard deviation of the property damage class distribution?

465

Assuming a normal distribution, 34.14% of all outcomes are within one standard deviation above the mean? What percentage is contained in the area between the mean and two standard deviations below the mean?

47.72%

Assume that the expected safe life of a heating element for a particular type of furnace is 4,000 hours. Which one of the following represents the chance that the heating element will become unsafe before being replaced?

50% because 50% of the normal distribution is below the 4,000 hour mean

Devon Company has noticed that the number of workers compensation claims each year at the company is normally distributed. If the predicted value of workers compensation claims for next year is 320 with a standard deviation of 30, what is the expected probability that between 290 and 350 workers compensation claims will occur?

68.3%

Blakely Company insures its fleet of vehicles under an auto policy with a $10,000 deductible for auto physical damage losses. Based on this information what is the probability that auto physical damage losses will be within the $10,000 deductible?

82.5%

In a normal distribution 34.13% of all outcomes are within one standard deviation above the mean. What percentage of the total outcomes is between two standard deviations below the mean and two standard deviations above?

95.44%

Probability analysis is particularly effective for projecting losses in organizations that have

A substantial volume of data on past losses and fairly stable operations

Probability analysis is best suited for organizations that have

A substantial volume of data on past losses.

The normal distribution is a probability distribution that, when graphed, generates a particular type of curve. Which one of the following best describes that curve?

Bell-shaped

A coefficient of variation is derived by

Dividing a distribution's standard deviation by its mean

A financial analyst wants to evaluate the effect that a predicted increase in the cost of steel will have on the net income of East Side Manufacturing. Which one of the following measurement techniques should the analyst use?

Earnings at risk

Which one of the following statements is true if earnings at risk are $200,000 with 90% confidence?

Earnings at risk are projected to be less than $200,000 10% of the time

A group of large life insurance companies pooled their mortality data over the past 25 years. Based on the pooled mortality data, a mortality table showing the probability of death at specified ages was developed. The insurers used these probabilities developed from the pooled mortality experience of the insurers are best described as

Empirical probabilities

Estimates whose accuracy depends on the size and representative nature of the samples being studied are

Empirical probabilities

Determining the probability that a certain event will occur can be an important part of exposure analysis in the risk management process. Which one of the following is the term used for probability that is developed based on actual experience?

Empirical probability

The weighted average of all of the possible outcomes of a probability distribution is the

Expected value

The weighted average of all the possible outcomes of a theoretical probability distribution is the

Expected value

Which one of the following is the term used for the weighted average of all the possible outcomes in a theoretical probability distribution?

Expected value

In using the coefficient of variation when comparing two distributions, if both distributions have the same mean, then the distribution with the larger standard deviation will have

Greater variability

Insurance and risk management professionals use measures of dispersion of the distributions of potential outcomes to gain a better understanding of loss exposures being analyzed. Which one of the following is true regarding the standard deviation of a distribution?

It indicates how widely dispersed the values in a distributions are.

Which one of the following best describes a probability distribution?

It represents probability estimates for a particular set of circumstances and the probability of each possible outcome

Which one of the following describes the law of large numbers?

It states that as the number of similar but independent exposure units increases, the relative accuracy of predictions about future outcomes also increases.

Which one of the following is a benefit of the conditional value at risk (CVaR) method?

It takes into account the extremely large losses that may occur.

An empirical probability is based on

historical data

Determining earnings-at-risk (EaR) entails modeling the influence of factors such as

Changes in the prices of products and production costs on an organization's earnings

Management of LMN Insurance Company is considering investing in the Stability-Growth Mutual Fund; however they are concerned about the volatility of the investment. The fund's manager said that on any given day, there is a 5% probability of losing more than 3% of the investment's worth. The statistic quoted by the fund manager is

Value-at-risk

Which one of the following statements is true regarding characteristics of normal distributions?

When graphed, a normal distribution generates a bell-shaped curve

In Fred's large landscaping business, he knows that there is a point where equipment becomes unsafe and difficult to maintain. Fred realizes that are 2,000 miles of use, his costs for maintenance on his large mowers and sod busters dramatically rise. Using probability analysis Fred can better know

When to replace equipment

Probability analysis would be most reliable for projecting losses in an org.

With a substantial volume of data on past losses

Even probability distribution includes the probability of

every possible outcome