Exam 7: Random Variables and Probability Distributions

At a large university students have either a final exam or a final paper at the end of a course. The table below lists the distribution of the number of final exams that students at the university will take, and their associated probabilities. What are the mean and standard deviation of this distribution?

While playing Monopoly, Laura estimated the probabilities of the non-zero rents according to the following probability distribution: Consider the random variable x = dollar amount in rent in a Monopoly roll. a) If the table above specifies the probability distribution f(x), what is the mean of the random variable x? b) If the probabilities are associated with the outcomes as in the table above, what is the standard deviation of the random variable x?

One common method used to forecast the results of elections is to take an "exit poll," asking people who they supported as they come out of the voting place. Suppose Smith and Jones are running for City Dogcatcher. In point of fact, 60% of the voting public in the neighborhood of the polling place support Smith. Assuming that the candidate of choice for a voter leaving the polling place is independent of the candidate of choice for the next person to leave, what is the probability that the first 5 voters to leave the polling place would have this sequence for candidate of choice? Smith, Smith, Smith, Jones, Smith

A gasoline tank for a certain model car is designed to hold 12 gallons of gas. Suppose that the actual capacity of the gas tank in cars of this type is well approximated by a normal distribution with mean 12.0 gallons and standard deviation 0.2 gallons. What is the probability that a randomly selected car of this model will have a gas tank that holds at most 11.7 gallons?

What information about a probability distribution do the mean and standard deviation of a random variable provide?