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Chapter 5: Problem 40
What are the parameters of the binomial probability distribution, and what do they mean?
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Which of the following are binomial experiments? Explain why. a. Rolling a die many times and observing the number of spots b. Rolling a die many times and observing whether the number obtained is even or odd c. Selecting a few voters from a very large population of voters and observing whether or not each of them favors a certain proposition in an election when \(54 \%\) of all voters are known to be in favor of this proposition.
In a poll, men and women were asked, "When someone yelled or snapped at you at work, how did you want to respond?" Twenty percent of the women in the survey said that they felt like crying (Time, April 4, 2011 ). Suppose that this result is true for the current population of women employees. A random sample of 24 women employees is selected. Use the binomial probabilities table (Table I of Appendix C) or technology to find the probability that the number of women employees in this sample of 24 who will hold the above opinion in response to the said question is A. at least 5 b. 1 to 3 c, at most 6
Many of you probably played the game "Rock, Paper, Scissors" as a child. Consider the following variation of that game. Instead of two players, suppose three players play this game, and let us call these players A, B, and C. Each player selects one of these three items - Rock, Paper, or Scissors - independent of each other. Player A will win the game if all three players select the same item, for example, rock. Player B will win the game if exactly two of the three players select the same item and the third player selects a different item. Player C will win the game if every player selects a different item. If Player \(\mathrm{B}\) wins the game, he or she will be paid \(\$ 1\). If Player \(C\) wins the game, he or she will be paid \(\$ 3\). Assuming that the expected winnings should be the same for each player to make this a fair game, how much should Player A be paid if he or she wins the game?
Indicate which of the following random variables are discrete and which are continuous. a. The amount of rainfall in a city during a specific month b. The number of students on a waitlist to register for a class c. The price of one ounce of gold at the close of trading on a given day d. The number of vacation trips taken by a family during a given year e. The amount of gasoline in your car's gas tank at a given time \(\mathbf{f}\). The distance you walked to class this morning
A fast food chain store conducted a taste survey before marketing a new hamburger. The results of the survey showed that \(70 \%\) of the people who tried this hamburger liked it. Encouraged by this result, the company decided to market the new hamburger. Assume that \(70 \%\) of all people like this hamburger. On a certain day, eight customers bought it for the first time. a. L.et \(x\) denote the number of customers in this sample of eight who will like this hamburger. Using the binomial probabilities table, obtain the probability distribution of \(x\) and draw a graph of the probability distribution. Determine the mean and standard deviation of \(x\). b. Using the probability distribution of part a, find the probability that exactly three of the eight customers will like this hamburger.
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