Seven performers A, B, C, D, E, F, and G are to appear in a fund raiser. The order of performance is determined by random selection. Find the probability that

$$\textbf{a.}\hspace{10pt}\text{D will perform first.}$$

$$\textbf{b.}\hspace{10pt}\text{E will perform sixth and B will perform last.}$$

$$\textbf{c.}\hspace{10pt}\text{The comedians will perform in the following order:C, D, B, A, G, F, E.}$$

$$\textbf{d.}\hspace{10pt}\text{CF or G will perform first.}$$

Arithmetic, Largest Value and Smallest Value) Write a program that inputs three different integers from the keyboard, then prints the sum, the average, the product, the smallest and the largest of these numbers. Use only the single-selection form of the if statement you learned in this chapter. The screen dialogue should appear as follows:

Enter three different integers: 13 27 14
Sum is 54
Average is 18
Product is 4914
Smallest is 13
Largest is 27

The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assign ing line positions on voting ballots. Among 4 l different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random selection so that they are equally likely to get that top line. Find the probability of 40 or more top lines for Democrats.

A job-performance evaluation form has these categories: 1=excellent; 2=good; 3=satisfactory; 4=poor; 5=unacceptable. Based on 15 client reviews, one employee had median rating of 4; mode rating of 1. The employee was pleased that most clients had rated her as excellent. The supervisor said improvement was needed because at least half the clients had rated the employee at the poor or unacceptable level. Comment on the different perspectives.

In 2012, the New York Yankees won 95 games and spent $\$ 198$ million on salaries for their players (USA Today). Is there a relationship between salary and team performance in Major League Baseball? For the 2012 season, a linear model fit to the number of Wins (out of 162 regular season games) from the team Salary $(\$ M)$ for the 30 teams in the league is:

$$\widehat{\text { Wins }}=76.45+0.046 \text { Salary. }$$

c) What does the slope mean in this context?

(a) Using a chart like the one shown, analyze the author's perspective in the selection.

$$\begin{aligned} &\text { Author's Perspective }\\ &\begin{array}{|l|l} \hline \text { Types of Details Included } & \text { Examples of Each } \\ \hline \square \text { researched facts } & \\ \square \text { personal experiences } & \\ \square \text { opinions } & \\ \square \text { attitudes } & \\ \hline \end{array} \end{aligned}$$

(b) Referring to your chart, briefly describe Cox's perspective.

Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door to door in the neighborhood, asking people to sign a petition. b) We want to know if students at our college are satisfied with the selection of food available on campus. We go to the largest cafeteria and interview every 10th person in line.

A freezer has a coefficient of performance of 2.40. The freezer is to convert 1.80 kg of water at $25.0^{\circ} \mathrm{C}$ to 1.80 kg of ice at $-5.0^{\circ} C$ in one hour. (a) What amount of heat must be removed from the water at $25.0^{\circ} C$ to convert it to ice at $-5.0^{\circ} C$? (b) How much electrical energy is consumed by the freezer during this hour? (c) How much wasted heat is delivered to the room in which the freezer sits?

Read the following selection from the reading and the questions below. Circle the letter of the correct answer to the question.

Los estudiantes que vienen al centro, pueden...

• investigar diferentes carreras
• buscar Información sobre cientos de universidades
• asistir a presentaciones sobre cómo financiar los estudios

What can a student do at the Career Center?

a. find out about careers and universities - b. find out about restaurants

Harbor seals, like many animals, determine the direction from 30 which a sound is coming by sensing the difference in arrival times at their two ears. A small difference in arrival times means that the object is in front of the seal; a larger difference means it is to the left or right. There is a minimum time difference that a seal can sense, and this leads to a limitation on a seal's direction sense. Seals can distinguish between two sounds that come from directions $3^{\circ}$ apart in air, but this increases to $9^{\circ}$ in water. Explain why you would expect a seal's directional discrimination to be worse in water than in air.

Express the answer to the following combination problem using combination notation $\left({ }_n C_k\right)$ and numerically. See the earlier examples.

Many lottery games are set up so that players select a subset of numbers from a larger set, and the winner is the person whose selection matches that chosen by some random mechanism. The order of the numbers is irrelevant. How many choices of six numbers can be made from the numbers 1 through 49?

Harbor seals, like many animals, determine the direction from which a sound is coming by sensing the difference in arrival times at their two ears. A small difference in arrival times means that the object is in front of the seal; a larger difference means it is to the left or right. There is a minimum time difference that a seal can sense, and this leads to a limitation on a seal's direction sense. Seals can distinguish between two sounds that come from directions $3 ^ { \circ }$ apart in air, but this increases to $9 ^ { \circ }$ in water. Explain why you would expect a seal's directional discrimination to be worse in water than in air.

In the 2008 baseball season, first baseman Ryan Howard of the Philadelphia Phillies led the Major Leagues with 48 home runs (HR) and 146 runs batted in (RBI). Overall, using all players with at least 300 plate appearances, the mean number of HR was $14.9$ with a standard deviation of $9.8$, whereas the mean number of RBI was $62.5$ with a standard deviation of $25.5$. Which was the more impressive PERFORMANCE? Explain, using the methods of this chapter.

Of the 281 players with at least 300 plate appearances in the 2008 Major League Baseball season, Jeff Mathis of the Los Angeles Angels had the lowest batting average ( $0.194)$ and Brad Wilkerson of the Toronto Blue Jays scored the fewest runs (21). Overall, the mean batting average was $0.272$, with a standard deviation of $0.027$, and the mean number of runs scored was $65.0$, with a standard deviation of 23.6. Which PERFORMANCE was worse? Explain, using the methods of this chapter.