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Chapter 7: Q 40. (page 462)

Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag

containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Let p^ be the proportion of vowels in her sample.

a. Is the 10% condition met in this case? Justify your answer.

b. Is the Large Counts condition met in this case? Justify your answer.

Short Answer

Expert verified

a. Yes.

b. No, large count condition is not met.

Step by step solution

01

Given Information

It is given that number of vowels is42and number of tiles are100.

02

Do 10% condition met in this case

Yes, it is met as7<10%of population size of100.

03

Do large count condition met

Population proportion is calculated as:

p=Population proportion=Number of vowelsNumber of tiles=42100=0.42

and n=7

Condition of normality is np≥10andn(1-p)≥10

Now, np=7(0.42)=2.94<10

and

n(1-p)=7(1-0.42)=4.06<10

Hence, large counts condition is not satisfied.

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Most popular questions from this chapter

Do you jog? The Gallup Poll asked a random sample of 1540 adults, "Do you happen to jog?" Suppose that the true proportion of all adults who jog is p=0.15. p=0.15.

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