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Chapter 5: Q 90. (page 331)

Common names The Census Bureau says that the 10 most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for 9.6% of all U.S. residents. Out of curiosity, you look at the authors of the textbooks for your current courses. There are 9 authors in all. Would you be surprised if none of the names of these authors were among the 10most common? (Assume that authors鈥� names are independent and follow the same probability distribution as the names of all residents.)

Short Answer

Expert verified

P(9notcommon)=40.32% not surprising

Step by step solution

01

Step 1. Given Information

The top ten most frequent names in the United States account for9.6% of all residents.

02

Step 2. Concept used

Multiplication rule: P(A鈭�B)=P(A鈭�B)脳P(B/A)

Complement rule: P(notA)=1鈭�P(A)

03

Step 3. Calculation

P(common)=9.6%=0.096

Complement rule:

P(notA)=1鈭�P(fail)=1鈭�0.096=0.904

Multiplication rule:

P(A鈭�B)=P(A)脳P(B)

Then it can calculate the likelihood of 9 uncommon names:

P(9notcommon)=(P(notcommon))9=(0.94)9鈮�0.4032=40.32%

Because the probability is larger than 5%, there is a good chance of getting 9 uncommon names, which is not unusual.

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Most popular questions from this chapter

Treating low bone density (4.2) Fractures of the spine are common and serious among women with advanced osteoporosis (low mineral density in the

bones). Can taking strontium ranelate help? A large medical trial assigned 1649 women to take either strontium ranelate or a placebo each day. All of

the subjects had osteoporosis and had had at least one fracture. All were taking calcium supplements and receiving standard medical care. The response variables were measurements of bone density and counts of new fractures over three years. The subjects were treated at 10 medical centers in 10 different countries.9 Outline an appropriate design for this experiment. Explain why this is the proper design.

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.

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).

Spinning a quarter With your forefinger, hold a new quarter (with a state featured on the reverse) upright, on its edge, on a hard surface. Then flick it with your other forefinger so that it spins for some time before it falls and comes to rest. Spin the coin a total of 25 times, and record the results.

(a) What鈥檚 your estimate for the probability of heads? Why?

(b) Explain how you could get an even better estimate.

Color-blind men Refer to Exercise 25. Suppose we randomly select 4 U.S. adult males. What鈥檚 the probability that at least one of them is red-green

color-blind? Design and carry out a simulation to answer this question. Follow the four-step process.
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