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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’ 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∩B)=P(A∩B)×P(B/A)

Complement rule: P(notA)=1−P(A)

03

Step 3. Calculation

P(common)=9.6%=0.096

Complement rule:

P(notA)=1−P(fail)=1−0.096=0.904

Multiplication rule:

P(A∩B)=P(A)×P(B)

Then it can calculate the likelihood of 9 uncommon names:

P(9notcommon)=(P(notcommon))9=(0.94)9≈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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