AP Statistics Unit 4, Part II Test

John maintains two separate lines of lobster traps in Penobscot Bay. The East Bay trap produces a mean of

34 pounds of lobsters per day with a standard deviation of 7 pounds. The West Bay trap produces a mean of

10 pounds of lobsters a day with a standard deviation of 4.5 pounds. The weight of lobsters produced by

each trap is independent of the other. Which of the following are the mean and approximate standard

deviation of the total weight of lobsters John traps in a day?

• Mean = 22 pounds; Standard deviation = 5.75 pounds

• Mean = 22 pounds; Standard deviation = 8.32 pounds

• Mean = 22 pounds; Standard deviation = 11.50 pounds

• Mean = 44 pounds; Standard deviation = 8.32 pounds

• Mean = 44 pounds; Standard deviation = 11.50 pounds

Answer explanation

An inspector examines a large shipment of several thousand laser pointers by randomly selecting and then inspecting 5 laser pointers. Suppose that 1% of the laser points are defective. Which one of the following expressions describes the probability that exactly one of the five laser pointers is defective?

• 
• 
• (0.01)^5

• (0.99)^5 (0.01)

• (5)(0.99)(0.01)

Answer explanation

At a carnival, a particular game requires the player to spin a wheel. When a child plays, the game operator allows them to continue to spin the wheel until they win a prize. Define X = the number of spins a child takes until they win a prize. Which, if any, of the following requirements for X to be a binomial random variable is violated in this setting?

• (A) There are two possible outcomes for each trial.

• (B) Each trial is independent of other trials.

• (C) The probability of “success” is the same for each trial.

• (D) The number of trials is fixed.

• (E) All requirements are met in this setting.

Answer explanation

Which of the following random variables is geometric?

• the number of baskets made in 20 free throws at a basketball game

• the number of text messages received in a one-hour period

• the number of times I have to roll a six-sided die to get two 6s

• the number of digits I will generate with a random number generator until I get a 4

• None of the above are geometric random variables.

Answer explanation

Which of the following is the probability that the insurance company will have to pay a claim of at least $1000 for a randomly selected car of this model?

• 0.05

• 0.13

• 0.32

• 0.37

• 0.40

Answer explanation

What is the expected value of C?

• $2650

• $2700

• $2770

• $3750

• $4057

Answer explanation

Which of the following is the best interpretation of the expected value E(C) that you found in Question 6?

• (A) If the company insures 10 cars of this model, they know they will incur 10×E(C) in costs.

• (B) The maximum cost to the company for insuring this car model is E(C) per car.

• (C) If the company insures a large number of these cars, they can expect the average cost per car to be approximately E(C).

• (D) The company must insure at least E(C) of these cars to make a profit.

• (E) If the company insures a large number of these cars, they can expect the variability in cost per car to average approximately E(C).

Answer explanation

The probability that a randomly selected crate has more than 4 contaminated chickens is

• 0.0851

• 0.2143

• 0.8889

• 0.7857

• 0.9999

Answer explanation

The mean and standard deviation of the number of contaminated chickens in a crate are

• μ = 2.4; σ = 2.16

• μ = 2.4; σ = 1.47

• μ = 6; σ = 2.24

• μ = 240; σ = 2.24

• μ = 240; σ = 5.04

Answer explanation

Find and interpret the standard deviation of W = the weighted average of the two measurements.

• 0.90. The weighted average tends to vary by about 0.90 meters from its mean of 100 meters.

• 0.90. The true weighted average tends to be 0.90 meters greater than the weighted average of the measurements.

• 0.640. The weighted average tends to vary by about 0.640 meters from its mean of 100 meters.

• 0.995. The true weighted average tends to be 0.995 meters greater than the weighted average of the measurements.

• 0.995. The weighted average tends to vary by about 0.995 meters from its mean of 100 meters.

Answer explanation