AP Statistics Chapter 6 Test

John maintains two separate lines of lobster traps in Penobscot Bay. The East Bay trap produces a mean of 12 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 11 pounds; Standard deviation = 11.50 pounds

• Mean = 11 pounds; Standard deviation = 8.32 pounds

An inspector examines a large shipment of several thousand laser pointers by randomly selecting and then inspecting 6 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 six laser pointers is defective?

• (9) (0.01) (0.99)

• (9)(0.01)(0.99)*

• (0.01)6

• (0.99) (0.01)

• (0.99)³ (0.01)

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?

Which of the following random variables is geometric?

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?

What is the expected value of C?

• $0

• $554

• $2770

• $3750

• $4057

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

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

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

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

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

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

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

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

It makes sense to give more weight to the less variable measurement because it is more likely to be closer to the truth. Consider the following weighted average W: W = = X₁ + X₂ 2 3 12 . 3 Find and interpret the standard deviation of W = the weighted average of the two measurements.

• 0.590. The weighted average tends to vary from its mean (100 meters) by about 0.590 meters.

• 0.590. The true weighted average tends to be 0.590 meters greater than the weighted average of the measurements.

• 0.873. The weighted average tends to vary from its mean (100 meters) by about 0.873 meters.

• 0.873. The true weighted average tends to be 0.873 meters greater than the weighted average of the measurements.

• 0.833. The weighted average tends to vary from its mean (100 meters) by about 0.833 meters.