Patients arriving at a hospital outpatient clinic can select one of three stations for service. Suppose that physicians are assigned randomly to the stations and that the patients therefore have no station preference. Three patients arrive at the clinic and their selection of stations is observed. List the sample points for the experiment.

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A hospital outpatient clinic performs four types of operations. The profit per operation, as well as the minutes of X-ray time and laboratory time used are given in Table 72. The clinic has 500 private rooms and 500 intensive care rooms. Type 1 and Type 2 operations require a patient to stay in an intensive care room for one day while Type 3 and Type 4 operations require a patient to stay in a private room for one day. Each day the hospital is required to perform at least 100 operations of each type. The hospital has set the following goals:

Goal 1: Earn a daily profit of at least $100,000.

Goal 2: Use at most 50 hours daily of X-ray time.

Goal 3: Use at most 40 hours daily of laboratory time. Table 72:$

$$\begin{matrix} \text{ } & \text{Type of Operation}\\ \text{ } & \text{1} & \text{2} & \text{3} & \text{4}\\ \text{Profit (\$)} & \text{200} & \text{150} & \text{100} & \text{80}\\ \text{X-ray time (minutes)} & \text{6} & \text{5} & \text{4} & \text{3}\\ \text{Laboratory time (minutes)} & \text{5} & \text{4} & \text{3} & \text{2}\\ \end{matrix}$$

$The cost per unit deviation from each goal is as follows:

Goal 1: Cost of$1 for each dollar by which profit goal is unmet

Goal 2: Cost of $10 for each hour by which X-ray goal is unmet

Goal 3: Cost of$8 for each hour by which laboratory goal is unmet Formulate a goal programming model to minimize the daily cost incurred due to failing to meet the hospital’s goals.

A survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs done in their homes. Half the complaints dealt with plumber A, who does 40% of the plumbing jobs in the town. Find the probability that a consumer will obtain a satisfactory plumbing job, given that the plumber was A.

Use the technology of your choice to do the following tasks. a. Obtain individual normal probability plots and the standard deviations of the samples. b. Perform a residual analysis. c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test on the data is reasonable. If so, also do parts (d)-(f). d. Use a one-way ANOVA test to decide, at the 5% significance level, whether the data provide sufficient evidence to conclude that a difference exists among the means of the populations from which the samples were taken. e. Interpret your results from part (d). f. If the result of the one-way ANOVA test is statistically significant, perform and interpret a Tukey multiple comparison. The U.S. Census Bureau collects information on incomes of employed persons and publishes the results in Historical Income Tables. Independent simple random samples of 100 employed persons in each of four age groups gave the data on annual income, in thousands of dollars, presented on the WeissStats CD.

An experiment that claimed to show that meditation lowers anxiety proceeded as follows. The experimenter interviewed the subjects and rated their level of anxiety. Then the subjects were randomly assigned to two groups. The experimenter taught one group how to meditate and they meditated daily for a month. The other group was simply told to relax more. At the end of the month, the experimenter interviewed all the subjects again and rated their anxiety level. The meditation group now had less anxiety. Psychologists said that the results were suspect because the ratings were not blind. Explain what this means and how lack of blindness could bias the reported results.

An experimenter interviewed subjects and rated their level of anxiety. Then, the subjects were randomly assigned to two groups. The experimenter taught one group how to meditate, and they meditated daily for a month. The other group was simply told to relax more. At the end of the month, the experimenter interviewed all the subjects again and rated their anxiety level. The meditation group now had less anxiety. Psychologists said that the results were suspect because the ratings were not blind. Explain what this means and why this is an important consideration in this experiment.

In a test to compare the effectiveness of two drugs designed to lower cholesterol levels, 75 randomly selected patients were given drug A and 100 randomly selected patients were given drug B. Those given drug A reduced their cholesterol levels by an average of 40 with a standard deviation of 12, and those given drug B reduced their levels by an average of 42 with a standard deviation of 15. The units are milligrams of cholesterol per deciliter of blood serum. Can you conclude that the mean reduction using drug B is greater than that of drug A?

Two gamblers bet $1 each on the successive tosses of a coin. Each has a bank of$6. What is the probability that one player—say, Jones—wins all the money on the tenth toss of the coin?

Four equally qualified people apply for two identical positions in a company. One and only one applicant is a member of a minority group. The positions are filled by choosing two of the applicants at random. Assign reasonable probabilities to the sample points.

Two gamblers bet $1 each on the successive tosses of a coin. Each has a bank of$6. What is the probability that they break even after six tosses of the coin?

Four equally qualified people apply for two identical positions in a company. One and only one applicant is a member of a minority group. The positions are filled by choosing two of the applicants at random. List the possible outcomes for this experiment.

Three imported wines are to be ranked from lowest to highest by a purported wine expert. That is, one wine will be identified as best, another as second best, and the remaining wine as worst. Assume that the “expert” really knows nothing about wine and randomly assigns ranks to the three wines. One of the wines is of much better quality than the others. What is the probability that the expert ranks the best wine no worse than second best?

Evaluate the integral.

$$\int _ { a } ^ { + \infty } \frac { x } { \left( x ^ { 2 } + 1 \right) ^ { 2 } } d x$$