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Chapter 5: Q 17. (page 295)

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

(a) According to a recent poll, 75% of American adults regularly recycle. To simulate choosing a random sample of 100 U.S. adults and seeing how many

of them recycle, roll a 4-sided die 100 times. A result of 1,2, or 3 means the person recycles; a 4 means that the person doesn鈥檛 recycle.

(b) An archer hits the center of the target with 60% of her shots. To simulate having her shoot 10 times, use a coin. Flip the coin once for each of the 10

shots. If it lands heads, then she hits the center of the target. If the coin lands tails, she doesn鈥檛.

Short Answer

Expert verified

Part (a) It is valid.

Part (b) It is not valid.

Step by step solution

01

Part (a) Step 1. Given Information  

The simulation designs are available for download. It is necessary to determine what is wrong with each of them.

02

Part (a) Step 2. Concept Used   

A simulation is a method of simulating random behaviour using a model that accurately reflects the circumstance, which is usually done with random numbers.

03

Part (a) Step 3. Explanation  

The simulation in the question is accurate. It's valid since the person recycles if they roll a 1,2, or 3, which corresponds to 3 of the 4 possible outcomes. As a result, 34=0.75=75% is implied. As a result, the simulation depicts a sample of people who recycle 75% at the time.

04

Part (b) Step 1. Explanation   

The simulation in the question isn't accurate. Because the coin has a50% probability of landing heads vs a 60%chance of reaching the goal, this is not a credible simulation. As a result, the simulation presented is invalid.

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Most popular questions from this chapter

Due to a hit, A very good professional baseball player gets a hit about 35% of the time over an entire season. After the player failed to hit safely in six straight at-bats, a TV commentator said, 鈥淗e is due for a hit by the law of averages.鈥� Is that right? Why?

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

(a) A roulette wheel has 38colored slots鈥�38 red, 18 black, and 2green. To simulate one spin of the wheel, let numbers 00 to 18 represent red, 19 to 37

represent black, and 38 to 40 represent green.

(b) About 10% of U.S. adults are left-handed. To simulate randomly selecting one adult at a time until you find a left-hander, use two digits. Let 01 to 10 represent being left-handed and 11 to 00 represent being right-handed. Move across a row in Table D, two digits at a time, skipping any numbers that have already appeared, until you find a number between 01 and 10. Record the number of people selected.

The birthday problem What鈥檚 the probability that in a randomly selected group of30 unrelated people, at least two have the same birthday? Let鈥檚 make two

assumptions to simplify the problem. First, we鈥檒l ignore the possibility of a February 29 birthday. Second, we assume that a randomly chosen person is equally likely to be born on each of the remaining 365 days of the year.

(a) How would you use random digits to imitate one repetition of the process? What variable would you measure?

(b) Use technology to perform 5 repetitions. Record the outcome of each repetition.

(c) Would you be surprised to learn that the theoretical probability is 0.71? Why or why not?

Stoplight On her drive to work every day, Ilana passes through an intersection with a traffic light. The light has a probability of 1/3 of being green when she gets to the intersection. Explain how you would use each chance device to simulate whether the light is red or green on a given day.

(a) A six-sided die

(b) Table D of random digits

(c) A standard deck of playing cards

Myspace versus Facebook A recent survey suggests that 85% of college students have posted a profile on Facebook, 54%use Myspace regularly, and 42% do both. Suppose we select a college student at random.

(a) Assuming that there are 20 million college students, make a two-way table for this chance process.

(b) Construct a Venn diagram to represent this setting.

(c) Consider the event that the randomly selected college student has posted a profile on at least one of these two sites. Write this event in symbolic form

using the two events of interest that you chose in (b).

(d) Find the probability of the event described in (c).

Explain your method.
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