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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

According to a survey, \(30 \%\) of adults are against using animals for research. Assume that this result holds true for the current population of all adults. Let \(x\) be the number of adults who are against using animals for research in a random sample of two adults. Obtain the probability distribution of \(x\). Draw a tree diagram for this problem.

An instant lottery ticket costs \(\$ 2 .\) Out of a total of 10,000 tickets printed for this lottery, 1000 tickets contain a prize of \(\$ 5\) each, 100 tickets have a prize of \(\$ 10\) each, 5 tickets have a prize of \(\$ 1000\) each, and 1 ticket has a prize of \(\$ 5000\). Let \(x\) be the random variable that denotes the net amount a player wins by playing this lottery. Write the probability distribution of \(x\). Determine the mean and standard deviation of \(x\). How will you interpret the values of the mean and standard deviation of \(x\) ?

What are the parameters of the binomial probability distribution, and what do they mean?

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.

The binomial probability distribution is symmetric for \(p=.50\), skewed to the right for \(p<.50\), and skewed to the left for \(p>.50\). Illustrate each of these three cases by writing a probability distribution table and drawing a graph. Choose any values of \(n\) (equal to 4 or higher) and \(p\) and use the table of binomial probabilities (Table I of Appendix \(\mathrm{C}\) ) to write the probability distribution tables.

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

A professional basketball player makes \(85 \%\) of the free throws he tries. Assuming this percentage holds true for future attempts, use the binomial formula to find the probability that in the next eight tries, the number of free throws he will make is a. exactly 8 b. exactly 5

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.

A household receives an average of \(1.7\) pieces of junk mail per day. Find the probability that this household will receive exactly 3 pieces of junk mail on a certain day. Use the Poisson probability distribution formula.