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Chapter 5: Q 18. (page 295)

Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.

(a) According to a recent survey, 50% of people aged 13 and older in the United States are addicted to email. To simulate choosing a random sample of

20people in this population and seeing how many of them are addicted to email, use a deck of cards. Shuffle the deck well, and then draw one card at a

time. A red card means that person is addicted to email; a black card means he isn鈥檛. Continue until you have drawn 20cards (without replacement) for the sample.

(b) A tennis player gets 95%of his second serves in play during practice (that is, the ball doesn鈥檛 go out of bounds). To simulate the player hitting 5second serves, look at pairs of digits going across a row in Table D. If the number is between 00and 94, the service is in; numbers between 95and 99indicate that the service is out.

Short Answer

Expert verified

Part (a) It isn't valid.

Part (b) It is valid.

Step by step solution

01

Part (a) Step 1. Given Information  

We must determine and justify the validity of each of the following simulation designs.

02

Part (a) Step 2. Concept Used    

A simulation is a technique for replicating random behaviour using a model that accurately reflects the situation, which is typically done with random numbers.

03

Part (a) Step 3. Explanation  

The simulation in the question isn't accurate. It is not valid because if the automobiles are not replaced, the chances of finding someone who is addicted to email are no longer 50%As a result, the replacement is required. If you draw a red card (addiction), for example, the next draw will have 25red cards and 26black cards, giving you a probability of 2525+26=2551=0.4902=49.02%And this isn't even half of it. As a result, the outcome.

04

Part (b) Step 1. Explanation    

The simulation in the question is accurate. It is legitimate since there are 95 possible outcomes ranging from 00 to 94 as well as five outcomes ranging from 95 to 99 As a result, the serve has a 95 out of 100 chance of being in, which translates to 95 percent of the time. As a result, the simulation is correct.

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Most popular questions from this chapter

Scrabble Refer to Exercise 20. About 3% of the time, the first player in Scrabble can 鈥渂ingo鈥� by playing all 7 tiles on the first turn. How many games

of Scrabble would you expect to have to play, on average, for this to happen? Design and carry out a simulation to answer this question. Follow the four step

process.

Simulation blunders Explain what鈥檚 wrong with each of the following simulation designs.

(a) According to the Centers for Disease Control and Prevention, about 26%of U.S. adults were obese in 2008. To simulate choosing 8adults at random and seeing how many are obese, we could use two digits. Let 01to 26represent obese and 27to 00represents not obese. Move across a row in Table D, two digits at a time, until you find 8 distinct numbers (no repeats). Record the number of obese people selected.

(b) Assume that the probability of a newborn being a boy is 0.5. To simulate choosing a random sample of 9babies who were born at a local hospital today and observing their gender, use one digit. Use ran dint (0,9) on your calculator to determine how many babies in the sample are male.

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 every100 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

Urban voters In the election described in Exercise 84, if the candidate鈥檚 predictions come true, what percent of her votes come from black voters? (Write this as a conditional probability and use the definition of conditional probability.)

Get rich A survey of 4826 randomly selected young adults (aged 19 to 25) asked, 鈥淲hat do you think are the chances you will have much more than a middle-class income at age 30?鈥� The two-way table shows the responses.

14 Choose a survey respondent at random.

(a) Given that the person selected is male, what鈥檚 the probability that he answered 鈥渁lmost certain鈥�?

(b) If the person selected said 鈥渟ome chance but probably not,鈥� what鈥檚 the probability that the person is female?

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