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Chapter 6: Q. 88 (page 404)

88. Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100tiles. There are 42vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses her7 tiles and is surprised to discover that all of them are vowels. Can we use a binomial distribution to approximate this probability? Justify your answer

Short Answer

Expert verified

No binomial distribution, because the draws are not independent and the constant probability of success is not constant.

Step by step solution

01

Given information

There are 42vowels, 56consonants, and 2blank tiles in the bag. Cait chooses her 7 tiles.

02

Explanation

A random variable has a binomial distribution if:

  • In terms of variables, there are two possible outcomes.
  • Each draw must be self-contained.
  • There are a set number of elements.
  • Probability of success is always the same.

The reason for this is that after selecting a tile, it is not returned to the bag and so cannot be selected again. As a result, the chances of winning after each tie are not the same.

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Most popular questions from this chapter

North Carolina State University posts the grade distributions for its courses online.3Students in Statistics 101in a recent semester received 26%A42%Bs,20%Cs,10%Ds,and2%Fs. Choose a Statistics 101student at random. The student鈥檚 grade on a four-point scale (with A=4) is a discrete random variable Xwith this probability distribution:

Sketch a graph of the probability distribution. Describe what you see .

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A large auto dealership keeps track of sales made during each hour of the day. Let X= the number of cars sold during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distribution of Xis as follows:

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