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The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor
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1 in 6 wins As a special promotion for its 20-ounce bottles of soda, a soft drink

Chapter 6, Problem 85

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QUESTION:

1 in 6 wins As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each cap. Some of the caps said, Please try again, while others said, Youre a winner! The company advertised the promotion with the slogan 1 in 6 wins a prize. Suppose the company is telling the truth and that every 20-ounce bottle of soda it fills has a 1-in-6 chance of being a winner. Seven friends each buy one 20-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize. (a) Explain why X is a binomial random variable. (b) Find the mean and standard deviation of X. Interpret each value in context. (c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the companys 1-in-6 claim inaccurate? Compute P(X 3) and use the result to justify your answer.

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QUESTION:

1 in 6 wins As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each cap. Some of the caps said, Please try again, while others said, Youre a winner! The company advertised the promotion with the slogan 1 in 6 wins a prize. Suppose the company is telling the truth and that every 20-ounce bottle of soda it fills has a 1-in-6 chance of being a winner. Seven friends each buy one 20-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize. (a) Explain why X is a binomial random variable. (b) Find the mean and standard deviation of X. Interpret each value in context. (c) The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or is the companys 1-in-6 claim inaccurate? Compute P(X 3) and use the result to justify your answer.

ANSWER:

Step 1 of 5

Given,

The probability of winning,

No. of friends,

X = the number who win a prize.

Let’s determine the following using these data:

 

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