AP Statistics Chapter 6

Which of the following could be considered binomial experiments?
I.  On each shot, a basketball player’s chance of scoring a free throw is estimated to be 0.38. The player tried 40 shots and the number of baskets is recorded.
II.  On a specific island, it has been determined that the probability is 0.12 that an inhabitant carries a certain defective gene. Inhabitants are tested until 10 with the defective gene are found.
III.  For a certain spinner, P(red) = 1/3, P(green) = 1/4, and P(blue) = 5/12. The spinner is spun 100 times and the number of each color is recorded.

• I only
• I and II
• I and III
• I, II, and III

On a physical fitness test middle school boys are awarded one point for each push-up they can do, and a point for each sit-up. National results showed that boys average 18 pushups with a standard deviation of 4 push-ups, and 34 sit-ups with standard deviation of 11. The mean of their combined (total) scores was therefore 18 + 34 = 52 points. What is the standard deviation of their combined scores?

• 5.3
• 11.7
• 15
• It cannot be determine

Binomial and geometric probability situation share all of the following conditions except one. Identify the choice that is not shared.

• The probability of success on each trial is the same.
• There are only two outcomes.
• The focus of the problem is the number of successes in a given number of trials.
• The probability of a success equals 1 minus the probability of a failure.

Which of the following random variables should be considered continuous?

• The number of brothers a randomly chosen person has
• The number of orders received by a mail order company in a randomly chosen week
• The number of cars owned by a randomly chosen adult male
• The time it takes a randomly chosen woman to run 100 meters

The weight of reports produced in a certain department has a Normal distribution with mean 60g and standard deviation 12g.  What is the probability that the next report will weigh less than 45g?

• 0.1042
• 0.1056
• 0.3944
• 0.0418

Caren is playing an instant lottery game.  What is the probability that she will not win until the 8^th try if the probability of winning is one out of 100 on a single try?

• 0.0009
• 0.0093
• 0.0933
• 0.9321

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

Let X represent the number on the face that lands up when a fair six-sided number cube is tossed. The expected value of X is 3.5 and the standard deviation of X is approximately 1.708. Two fair six-sided number cubes will be tossed, and the numbers appearing on the faces that land up will be added. Which of the following values is closest to the standard deviation of the resulting sum?

• 1.708
• 1.848
• 2.415
• 3.416

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4 and if the number of spots showing is 1, 2 or 3, you win nothing. Let X be the amount you win.  What is the expected value of X?

• $
• $1
• $2.50
• $4

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4 and if the number of spots showing is 1, 2 or 3, you win nothing. Let X be the amount you win. What is the standard deviation of X?

• $1
• $1.35
• $1.41
• $1.78