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Chapter 5: Q 16. (page 295)

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.

Short Answer

Expert verified

Part (a) The Simulation is incorrect.

Part (b) In the Simulation, they're almost correct.

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   

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between 0 (never happens) and 1 (happens frequently) (always occurs).

03

Part (a) Step 3. Explanation    

Looking at the question's stimuli, we can conclude that repeats should be permitted in this simulation because if you don't, the probability of 26% for obesity will no longer be accurate after the first two-digit number. As a result, the repeats are missing in this simulation, indicating that something is wrong with it.

04

Part (b) Step 1. Explanation   

We can deduce from the simulation provided in the question that the command randlnt(0,9)means that a number between 0 and 9 would be picked at random, and hence digits 0 and 9 are all equally likely to be drawn. Receiving four males in a sample of nine newborns, on the other hand, should not be significantly more likely than obtaining zero boys.

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Most popular questions from this chapter

Mac or PC? A recent census at a major university revealed that40% of its students primarily used Macintosh computers (Macs). The rest mainly used

PCs. At the time of the census, 67% of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students who said that they used PCs as their

main computers. Suppose we select a student at random from among those who were part of the census.

(a) Assuming that there were 10,000 students in the census, 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 student is a graduate student who uses a Mac. 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.

Playing cards Shuffle a standard deck of playing cards and deal one card. Define events J: getting a jack, and R: getting a red card.

(a) Construct a two-way table that describes the sample space in terms of events J and R.

(b) Find P(J) and P(R).

(c) Describe the event 鈥�J and R鈥� in words. Then find P(JandR)

(d) Explain why P(JorR)鈮�P(J)+P(R) Then use the general addition rule to compute P(JorR).

Rolling a die The following figure displays several possible probability models for rolling a die. We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not legitimate. That is, they do not obey the rules. Which are legitimate and which are not? In the case of the illegitimate models, explain what is wrong.

Urban voters The voters in a large city are 40%white, 40%black, and 20%Hispanic. (Hispanics may be of any race in official statistics, but here we are speaking of political blocks.) A mayoral candidate anticipates attracting 30%of the white vote, 90%of the black vote, and 50%of the Hispanic vote. Draw a tree diagram to represent this situation. What percent of the overall vote does the candidate expect to get? Use the four-step process to guide your work.

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