Besides their known long-term effects, do cigarettes also cause short-term illnesses such as colds? To help answer this question, a sample of smokers was drawn. Each person was asked to report the average number of cigarettes smoked per day and the number of days absent from work due to colds last year. Determine the regression line

A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits-clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2.3, +, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as "face cards." Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.

$$\text{Type of card}\\ \text{Suit} \begin{array}{l|c|c|c} & \text { Face card } & \begin{array}{c} \text { Nonface } \\ \text { card } \end{array} & \text { Total } \\ \hline \text { Heart } & 3 & 10 & 13 \\ \hline \text { Nonheart } & 9 & 30 & 39 \\ \hline \text { Total } & 12 & 40 & 52 \end{array}$$

Are the events "heart" and "face card" independent? Justify your answer.

An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs-with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is a. a spade? b. red? c. not a club?

A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits- clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, queen, and king. The jacks, queens, and kings are referred to as "face cards." Imagine that we shuffle the deck thoroughly and deal one card. Define events F: getting a face card and H: getting a heart. The two-way table summarizes the sample space for this chance process.

$$\begin{array}{ccc} & \text{Card} \\ \text{Suit} & {\begin{array}{l|c|c|c} & \text { Face card } & \text { Nonface card } & \text { Total } \\ \hline \text { Heart } & 3 & 10 & 13 \\ \hline \text { Nonheart } & 9 & 30 & 39 \\ \hline \text { Total } & 12 & 40 & 52 \end{array}} \\ \end{array}$$

Find $P\left(H^{C}\right.$ and $\left.F\right).$ Interpret this value in context.

A normal pack of playing cards contains 52 cards. These are made up of four suits (hearts, diamonds, clubs and spades. Each suit consists of 13 cards. These are labelled Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King. The hearts and diamonds are red; the clubs and spades are black. If a card is picked at random from a normal pack of cards, calculate the probability of picking: a) a heart, b) not a heart, c) a 4, d) a red King, e) a Jack, Queen or King, f) the Ace of spades, g) an even numbered card, h) a 7 or a club.

A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits-clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jack, queen, and king are referred to as "face cards." Imagine that we shuffle the deck thoroughly and deal one card. Let's define events F: getting a face card and H: getting a heart. The two-way table summarizes the sample space for this chance process. $$ \text{Card} \\ \begin{array}{l|c|c|c} && \text { Face card } & \text { Nonface card } & \text { Total } \\ \hline &\text { Heart } & 3 & 10 & 13 \\ \text{Suit} & \hline \text { Nonheart } & 9 & 30 & 39 \\ \hline &\text { Total } & 12 & 40 & 52 \end{array} $$ Find $P\left(\mathrm{H}^{\mathrm{C}} \text { or } \mathrm{F}\right).$

In a standard deck of playing cards, there are four suits (red suits = hearts and diamonds, black suits = spades and clubs). Each suit has thirteen cards: Ace (A), 2, 3, 4, 5, 6, 7, 8, 9, 10, and the face cards Jack (J), Queen (Q), and King (K). In a single draw, what is the probability that you will draw a face card? A red card? A red face card?

The regression line relating verbal SAT scores and college GPA is Average GPA = 0.539 + 0.00362 (Verbal SAT)

Estimate the average GPA for those with verbal SAT scores of 600.

"Ecstasy" was a popular drug in the 1990s. It produced a sense of euphoria derisively called the "yuppie high." One investigator made a careful sample survey to estimate the prevalence of drug use at Stanford University. Two assistants were stationed on the main campus plaza and instructed to interview all students who passed through at specified times. As it turned out, 39% of 369 students interviewed said they had used Ecstasy at least once. Does the investigator's procedure give a probability sample of Stanford students? Answer yes or no, and explain.

A survey is carried out by the finance department to determine the distribution of household size in a certain city. They draw a simple random sample of 1,000 households. After several visits, the interviewers find people at home in only 653 of the sample households. Rather than face such a high non-response rate, the department draws a second batch of households, and uses the first 347 completed interviews in the second batch to bring the sample up to its planned strength of 1,000 households. The department counts 3,087 people in these 1,000 households, and estimates the average household size in the city to be about 3.1 persons. Is this estimate likely to be too low, too high, or about right? Why?

The San Francisco Chronicle reported on a survey of top high-school students in the U.S. According to the survey, Cheating is pervasive. Nearly 80 percent admitted some dishonesty, such as copying someone's homework or cheating on a exam. The survey was sent last spring to 5,000 of the nearly 700,000 high achievers included in the 1993 edition of Who's Who Among American High School Students. The results were based on the 1,957 completed surveys that were returned. "The survey does not pretend to be representative of all teenagers," said Who's Who spokesman Andrew Weinstein. "Students are listed in Who's Who if they are nominated by their teachers or guidance counselors. Ninety-eight percent of them go on to college."a) Why isn't the survey "representative of all teenagers"? b) Is the survey representative "of the nearly 700,000 high achievers included in the 1993 edition of Who's Who Among American High School Students"? Answer yes or no, and explain briefly.

One hospital has 218 live births during the month of January. Another has 536. Which is likelier to have 55% or more male births? Or is it equally likely? Explain. (There is about a 52% chance for a live-born infant to be male.)

One hundred draws are made at random with replacement from a box with ninety-nine tickets marked "0" and one ticket marked "1". True or false, and explain: a) The sum will be around 1, give or take 1 or so. b) There is about a 68% chance that the sum will be in the range 0 to 2.

A programmer is working on a new program, COIN, to simulate tossing a coin. As a preliminary test, he sets up the program to do one million tosses. The program returns with a count of 502,015 heads. The programmer looks at this and thinks: Hmmm. Two thounsand and fifteen off. That's a lot. No, wait. Compare it to the million. Two thousand---forget the fifteen---out of a million is two out of a thousand. That's one in five hundred. One fifth of a percent. Very small. Good. COIN passes. Do you agree? Answer yes or no, and explain.