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Lotto In the United Kingdom鈥檚 Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought one ticket for herself and one for each of her four adult children. She had the lottery computer randomly select the six numbers on each ticket. When the six winning numbers were drawn, Rosemary was surprised to find that none of these numbers appeared on any of the five Lotto tickets she had bought. Should she be? Design and carry

out a simulation to answer this question. Follow the four-step process.

Random assignment Researchers recruited $20$惫辞濒耻苍迟别别谤蝉鈥�$8$men and $12$women鈥攖o take part in an experiment. They randomly assigned the subjects

into two groups of $10$people each. To their surprise, $6$of the $8$men were randomly assigned to the same treatment. Should they be surprised? Design and carry out a simulation to estimate the probability that the random assignment puts $6$or more men in the same group. Follow the four-step

process.

Genetics Suppose a married man and woman both carry a gene for cystic fibrosis but don鈥檛 have the disease themselves. According to the laws of genetics, the probability that their first child will develop cystic fibrosis is $0.25$

(a) Explain what this probability means.

(b) Why doesn鈥檛 this probability say that if the couple has $4$ children, one of them is guaranteed to get cystic fibrosis?

Taking the train According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time. To test this claim, an auditor chooses 6 weekdays at random during a month to ride this train. The train arrives late on 2 of those days. Does the auditor have convincing evidence that the company鈥檚 claim isn鈥檛 true? Design and carry out a simulation to answer this question. Follow the four-step process.

You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about $0.11$ This means that (a) in every$100$ bridge deals, each player has one ace exactly $11$ times.

(b) in one million bridge deals, the number of deals on which each player has one ace will be exactly $110,000$

(c) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to $11\%$

(d) in a very large number of bridge deals, the average number of aces in a hand will be very close to $0.11$

(e) None of these

If I toss a fair coin five times and the outcomes are $\left\{TTTTT\right\}$, then the probability that tails appears on the next toss is (a) 0.5. (b) less than $0.5$ (c) greater than $0.5$ (d) $0$ (e) $1$ Exercises $33$ to $35$ refer to the following setting. A basketball player makes $47\%$ of her shots from the field during the season.

Use the correct choice from the previous question and these random digits to simulate 10 shots:$8273471490204674751181676553009438314893$How many of these 10 shots are hits? (a) $2$(b) $3$(c) $4$(d) $5$(e) $6$

Ten percent of U.S. households contain $5$or more people. You want to simulate choosing a household at random and recording whether or not it contains $5$or

more people. Which of these are correct assignments of digits for this simulation? (a) Odd = Yes ($5$or more people); Even = No (not $5$or more people)

(b) $0$= Yes; $1,2,3,4,5,6,7,8,9$= No

(c) $5$= Yes; $0,1,2,3,4,6,7,8,9$= No

(d) All three are correct.

(e) Choices (b) and (c) are correct, but (a) is not.

Are you feeling stressed? (4.1) A Gallup Poll asked whether people experienced stress 鈥渁 lot of the day yesterday.鈥� Forty percent said they did. Gallup鈥檚 report said, 鈥淩esults are based on telephone interviews with $178,545$ national adults,

aged $18$ and older, conducted Jan. $2鈥�June30,2009.鈥�4$

(a) Identify the population and the sample.

(b) Explain how undercover could lead to bias in this survey.

Waiting to park (1.3) Do drivers take longer to leave their parking spaces when someone is waiting? Researchers hung out in a parking lot and collected

some data. The graphs and numerical summaries below display information about how long it took drivers to exit their sp\aces.

(a) Write a few sentences comparing these distributions.

(b) Can we conclude that having someone waiting causes drivers to leave their spaces more slowly? Why or why not?