Exam 6: Discrete Random Variables

According to data from the state blood program, 40 percent of all individuals have group A blood. If six individuals give blood, find the probability that exactly three of the individuals have group A blood.

The J.O. Supplies Company buys calculators from a non-U.S. supplier. The probability of a defective calculator is 10 percent. If 3 calculators are selected at random, what is the probability that one of the calculators will be defective?

The mean of the binomial random variable is np(1 − p).

Three candidates run for different offices in different cities. Each has a one in three chance of being elected in his/her city. What is the probability that at least one of them will be elected?

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that no more than one bankruptcy occurs next month.

Historical data for a local manufacturing company show that the average number of defects per product produced is 2. In addition, the number of defects per unit is distributed according to a Poisson distribution. What is the probability that there will be a total of 7 defects on four units?

The variable Employment Status, which can take either the value 1 for Employed or 0 for Unemployed, is an example of a ________ random variable.

In a hypergeometric probability distribution of a population of N items, r refers to the number of successes and N − r refers to the number of failures.

If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question, then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution.

According to data from the state blood program, 40 percent of all individuals have group A blood. Suppose that of six randomly selected individuals, three have group A blood. Would you believe the data from the state blood program?

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). Determine the expected number of heads.

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw, how much would you expect to win on average?

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-through fast-food restaurant is 3 cars in 10 minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues. If 6 college freshmen are randomly selected, find the probability that only 1 supports increased spending on environmental issues.

If x is a Poisson random variable with a mean of 10, what is the probability that x is equal to 8?

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every two hours. Assume that the patient arrivals are distributed according to a Poisson distribution. Determine the probability of 6 patients arriving in a five-hour period.

In the context of the hypergeometric distribution, r is

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues. If 6 college freshmen are randomly selected, find the probability that fewer than 4 support increased spending on environmental issues.

A Poisson random variable is a continuous variable that can be used to describe the number of occurrences of an event over a specified interval of time or space.

The distribution whose mean is equal to its variance is the ________ distribution.