Deck 6: Random Variables and Discrete Probability Distributions

Question 1

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

A) discrete.
B) continuous.
C) compact.
D) predictable.

Answer 1

discrete.

Question 2

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?

A) 9.99 × 10-88
B) 0.9714
C) 9.97 × 10-5
D) 9.91 × 10-4

Answer 2

9.97 × 10-5

Question 3

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

A) unique number generator (UNG).
B) outcome assigning function (OAF).
C) random variable (RV).
D) random vehicle (RV).

Answer 3

random variable (RV).

Question 4

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?

A) 0.6702
B) 0.3412
C) 0.3298
D) 0.6588

Question 5

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?

A) 0.421
B) 0.617
C) 0.383
D) 0.579

Question 6

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

A) binomial distribution.
B) hypergeometric distribution.
C) Poisson distribution.
D) geometric distribution.

Question 7

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

A) 0.124
B) 0.976
C) 0.876
D) Need more information to answer.

Question 8

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?

A) 2.19
B) 4.80
C) 1.48
D) 3.14

Question 9

Eighty percent of the people who see a particular movie love it and plan to see it again soon.If we randomly select 18 people who are exiting the movie theater after seeing this movie, what is the probability that fewer than 12 loved the movie and will plan to see it again soon?

A) 0.0513
B) 0.9487
C) 0.1329
D) 0.8671

Question 10

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

A) discrete.
B) continuous.
C) compact.
D) predictable.

Question 11

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

A) All possible values of the random variable and their associated probability
B) All possible experimental outcomes and their associated probability
C) All values of the random variable and all experimental outcomes
D) All values of the random variable and the probability of each experimental outcome

Question 12

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) 0.9920
B) 0.0189
C) 0.1029
D) 0.0081

Question 13

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?

A) $0
B) $2
C) -$2
D) $5

Question 14

We define random variable X as a count of shoppers who use the "self-scan" aisle at the local supermarket during the day.X is a(n) ________________ random variable.

A) predictable
B) unpredictable
C) continuous
D) discrete

Question 15

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?

A) 0.0010
B) 0.1901
C) 0.8670
D) 0.1330

Question 16

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

A) a hypergeometric random variable.
B) a geometric random variable.
C) a Poisson random variable.
D) a binomial random variable.

Question 17

An experiment consists of tossing a balanced coin three times.Each individual coin toss results in either a heads (H) or a tails (T).We define a random variable ( ) as a count of heads from a given trial.How many experimental outcomes result in ?

A) 2
B) 1
C) 3
D) 0

Question 18

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) A binomial random variable would be accurate as long as the sampling process used is identical for each trial.
B) A geometric random variable would be better in this situation because the population is small and the sampling is without replacement.
C) A hypergeometric random variable would be better in this situation because the population is small and the sampling is without replacement.
D) A supergeometric random variable would be better in this situation because the population is small and the sampling is without replacement.

Question 19

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.

A) continuous
B) unpredictable
C) predictable
D) discrete

Question 20

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) 0.4654
B) 0.3814
C) 0.5346
D) 0.5248

Question 21

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?

A) 0.0017
B) 0.0004
C) 0.4800
D) 0.0480

Question 22

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.

A) 114
B) 229
C) 320
D) 457

Question 23

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?

A) 0.0898
B) 0.4898
C) 0.5112
D) 0.9102