The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.

$$\begin{matrix} \text{Payment (\$)} & \text{Probability}\\ \text{0} & \text{0.85}\\ \text{500} & \text{0.04}\\ \text{1000} & \text{0.04}\\ \text{3000} & \text{0.03}\\ \text{5000} & \text{0.02}\\ \text{8000} & \text{0.01}\\ \text{10000} & \text{0.01}\\ \end{matrix}$$

Use the expected collision payment to determine the collision insurance premium that would enable the company to break even.

The following table provides a probability distribution for the random variable x.

$$\begin{matrix} \text{x} & \text{f(x)}\\ \text{3} & \text{0.25}\\ \text{6} & \text{0.5}\\ \text{9} & \text{0.25}\\ \end{matrix}$$

Compute $E ( x )$ , the expected value of $x$ .

To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.

List the experimental outcomes associated with performing the blood analysis.

Automobile collision insurance is used to pay for any claims made against the driver in the event of an accident. This type of insurance will typically pay to repair any assets that your vehicle damages.

Collision claims tend to be skewed right. Why do you think this is the case?

The budgeting process for a midwestern college resulted in expense forecasts for the coming year (in $millions) of$9, $10,$11, $12, and$13. Because the actual expenses are unknown, the following respective probabilities are assigned: .3, .2, .25, .05, and .2.

Show the probability distribution for the expense forecast.

The Mountain States Office of State Farm Insurance Company reports that approximately 85% of all automobile damage liability claims are made by people under 25 years of age. A random sample of five automobile insurance liability claims is under study. Find the mean and standard deviation of this probability distribution. For samples of size 5, what is the expected number of claims made by people under 25 years of age?

The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medicare service. For this group, $40\%$ of first-round appeals were successful (The Wall Street Journal, October 22, 2012). Suppose 10 first-round appeals have just been received by a Medicare appeals office. a. Compute the probability that none of the appeals will be successful.

The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand.

$$\begin{matrix} \text{Unit Demand} & \text{Probability}\\ \text{300} & \text{0.2}\\ \text{400} & \text{0.3}\\ \text{500} & \text{0.35}\\ \text{600} & \text{0.15}\\ \end{matrix}$$

If the company bases monthly orders on the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product?

The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).

$$\begin{matrix} \text{ } & \text{ } & \text{Probability} & \text{ }\\ \text{Job Satisfaction} & \text{IS Senior} & \text{ } & \text{IS Middle}\\ \text{Score} & \text{Executives} & \text{ } & \text{Managers}\\ \text{1} & \text{0.05} & \text{ } & \text{0.04}\\ \text{2} & \text{0.09} & \text{ } & \text{0.1}\\ \text{3} & \text{0.03} & \text{ } & \text{0.12}\\ \text{4} & \text{0.42} & \text{ } & \text{0.46}\\ \text{5} & \text{0.41} & \text{ } & \text{0.28}\\ \end{matrix}$$

What is the expected value of the job satisfaction score for senior executives?

The following table provides a probability distribution for the random variable x.

$$\begin{matrix} \text{x} & \text{f(x)}\\ \text{3} & \text{0.25}\\ \text{6} & \text{0.5}\\ \text{9} & \text{0.25}\\ \end{matrix}$$

Compute $\sigma ,$ the standard deviation of $x$ .

An insurance company charges an annual premium of $75 for a$200,000 insurance policy against a house burning down. If the (empirical) probability that a house burns down in a given year is .0003, what is the expected value of the policy to the insurance company?

Given below is a bivariate distribution for the random variables x and y.

$$\begin{array}{ccc} \boldsymbol{f}(\boldsymbol{x}, \boldsymbol{y}) & \boldsymbol{x} & \boldsymbol{y} \\ .2 & 50 & 80 \\ .5 & 30 & 50 \\ .3 & 40 & 60 \end{array}$$

e. Is the variance of the sum of $x$ and $y$ bigger than, smaller than, or the same as the sum of the individual variances? Why?

The following table is a partial probability distribution for the MRA Company’s projected profits (x  profit in $1000s) for the first year of operation (the negative value denotes a loss).

$$\begin{matrix} \text{x} & \text{f(x)}\\ \text{100} & \text{0.1}\\ \text{0} & \text{0.2}\\ \text{50} & \text{0.3}\\ \text{100} & \text{0.25}\\ \text{150} & \text{0.1}\\ \text{200}\\ \end{matrix}$$

What is the proper value for f (200)? What is your interpretation of this value?

Reread The Case of the Nonstop Car. Assume that the accident happened in a state without no-fault insurance and that both Terrell and Candace had insurance coverage. Each had a policy covering all types of losses that included a $\$ 250$ deductible for collision insurance. Also assume that Terrell was at fault.

If the damages were less than the policy's limits, would Terrell have to pay any money to get his car fixed?