Exam 6: Random Variables and Discrete Probability Distributions

Your car breaks down in a remote location.Your cell phone has enough power left in it to send four text messages.If there is a 30% chance that any text you send will be read by the recipient, what is the probability that you will need to send all four texts to reach help (i.e., the probability that your fourth text will be the first and only one read)?

A random variable that can assume only a finite number of values or countably infinite values is said to be:

In a recent production batch of automobiles, 10% are found to have a minor engine defect.A rental car company purchases 20 of these vehicles.What is the probability that exactly 3 of the 20 purchased vehicles are defective?

The number of traffic accidents per day on a certain section of highway is thought to be a Poisson distribution with a mean of 2.19 accidents.What is the standard deviation of the number of accidents?

Suppose that in a population of 1000 items, there are 300 defective items and 700 items that are not defective.If you select two items at random from this population, what is the probability that both will be defective?

When sampling without replacement, the appropriate probability distribution is a:

An experiment that consists of n identical, independent trials, each with only two mutually exclusive outcomes that have constant probabilities, may be modeled with:

What two things must a probability distribution for a random variable display?

If P(X > 7) = 0.124, what is the probability of P(X 7)?

We play a game of chance using a deck of 52 playing cards.Four of the cards are aces.If we randomly draw five cards with replacement (i.e., draw card 1, record its value, put it back in the deck, shuffle, draw card 2, etc.), what is the probability that at least one of the cards is an ace?

At a particular spot in a local lake, there are, on average, 25 fish per cubic meter.If we assume that the probability of finding a fish is the same in this region over all cubic meters of water and that the number of fish in any one cubic meter in this region is independent of the number in any other cubic meter, what is the probability that we will find exactly 12 fish in the cubic meter in which we are fishing?

Researchers were interested in whether uniform colors give athletes an advantage.To investigate this question, they considered 457 boxing, tae kwon do, Greco-Roman wrestling, and freestyle wrestling matches in the 2004 Olympic Games, in which the competitors were randomly assigned to wear either red or blue.We can model this situation with a binomial random variable X = number of wins by players wearing red.If we assume that uniform color has no effect on the competitor's chances of winning, and that the matches are independent, what is the expected number of matches won by the players wearing red in this situation? Round up to the nearest whole number.

Mars Corporation (the manufacturer of Skittles) states that 20% of all Skittles candies produced are lime-flavored.Suppose we randomly draw 25 Skittles from a bag.What is the probability that fewer than five are lime-flavored?

In a game of chance, two pyramid-shaped, four-sided dice are rolled and their individual totals are added.The probability distribution for the game appears in the table. ​ ​ If the sum of the two four-sided dice exceeds 5 (result from die 1 + result from die 2 > 5), the roller wins $5 (end result +5).If the sum is 5 or less, the roller loses $3 (end result -3).What is the expected value from this game?

At the school playground, students can check out 20 red playground balls to play with.Eight of the balls are of superior quality and bounce well enough to support a decent game of double four square.If we need two of the superior-quality balls to play the game and the four players each randomly select a playground ball to check out, what is the probability that we will be able to have a decent game (i.e., have at least two superior-quality balls)?

A function that assigns a unique numerical value to each outcome in a sample space is known as a(n):

We define random variable Y as the number of defective products a particular assembly line produces in a day.Y is a(n) ________________ random variable.

We wish to model a sampling situation from a population of 100 samples, where each will be evaluated as either a success or a failure.The proportion of "successes" in the population is known, and a sample without replacement is to be selected.It is proposed to use a binomial random variable to model probability in this model.Which of the following statements is accurate concerning this situation?

A random variable that can assume any value within its interval is said to be:

A computer programmer is writing a program that will solicit individuals to fill out a research questionnaire on why people answer unsolicited email requests.The program will randomly contact subscribers until someone responds positively.After the first response, the program redirects to the questionnaire and shuts down.If there is a 99.99% non-response rate, what is the probability that the program will send out 30 emails before shutting down?