Probability Review

A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X-Y?

• 24.0

• 17.5

• 12.0

• 6.0

• 4.9

The distribution of colors in a candy bag is given. If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?

• 0.09

• 0.22

• 0.25

• 0.75

• 0.78

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language and a psychology course?

• 0.45

• 0.32

• 0.20

• 0.13

• 0.05

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 a.m., what is the probability that the student will arrive at the college campus later than 9 a.m.?

• 0.16

• 0.32

• 0.50

• 0.84

• 1.00

A popular computer card game keeps track of the number of games played and the number of games won on that computer. The cards are shuffled before each game, so the outcome of the game is independent from one game to the next and is based on the skill of the player. Let X represent the number of games that have been won out of 100 games. Under which of the following situations would X be a binomial random variable?

• All games were played by the same player, whose skill improved over the course of the 100 games.

• A group of 5 players of different skill levels were each allowed to play 20 games in a row.

• A group of players of different skill levels were each allowed to play until they had lost 3 games and this resulted in 100 games played.

• Two players of equal skill level each played one game a day for 50 days and their skill level did not change from day to day.

• Two players of different skill levels competed by allowing one player to continue until a game was lost, then the other player to continue until a game was lost, and so on, until 100 games were played.

For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected from the airport in January, what is the probability that the flight will have at least one of the two types of delays?

• 0.065

• 0.335

• 0.350

• 0.450

• 0.665

A contestant's final winnings on a game show are determined by a random selection of a base amount and a possible multiplier. For the base amount, the contestant randomly selects one of four cards, where two cards are marked $1,000, one card is marked $2,000, and one card is marked $5,000. After choosing the card, the contestant randomly selects one of five chips, where three chips are red and two chips are white. If the selected chip is red, the contestant's final winnings are twice the value of the base amount. If the selected chip is white, the contestant's final winnings are the value of the base amount. What is the probability that a contestant's final winnings are exactly $2,000?

• 0.100

• 0.200

• 0.250

• 0.325

• 0.400

A produce supplier ships boxes of produce to individual customers. The distribution of weights of shipped boxes is approximately normal with mean 36 pounds and standard deviation 4 pounds. Which expression represents the weight, in pounds, at the 75th percentile of the distribution?

• -1.96(4)+36

• -0.25(4)+36

• 0.25(4)+36

• 0.67(4)+36

• 0.75(4)+36

• Event A and event B are mutually exclusive and are independent.

• Event A and event B are mutually exclusive and are NOT independent.

• Event A and event B are NOT mutually exclusive and are independent.

• Event A and event B are NOT mutually exclusive and are NOT independent.

• Event A and event B are NOT mutually exclusive and independence can not be determined with the information given.

The random variable X is normally distributed with mean 5 and standard deviation 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and standard deviation of Y?

• The mean is 20 and the standard deviation is 102.

• The mean is 20 and the standard deviation is 50.

• The mean is 22 and the standard deviation is 102.

• The mean is 22 and the standard deviation is 100.

• The mean is 22 and the standard deviation is 50.