Question

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

a. Yes.

b. No, large count condition is not met.

Step-by-step solution

Given Information

It is given that number of vowels is$42$and number of tiles are$100$.

Do 10% condition met in this case

Yes, it is met as$7<10\%$of population size of$100$.

Do large count condition met

Population proportion is calculated as:

$p=\text{Population proportion}=\frac{\text{Number of vowels}}{\text{Number of tiles}}=\frac{42}{100}=0.42$

and $n=7$

Condition of normality is $np\ge 10\text{and}n(1-p)\ge 10$

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.