AP Stats - Unit 6 Review

A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?

• $332.00

• $432.00

• $532.00

• $1,343.75

• $1,400.00

A nonprofit organization plans to hold a raffle to raise funds for its operations. A total of 1,000 raffle tickets will be sold for $1.00 each. After all the tickets are sold, one ticket will be selected at random and its owner receives $50.00. The expectation value for the next gain of each ticket is -$0.95. What is the meaning of this expected value in context?

• The ticket owners lose an average of $0.05 per raffle ticket.

• The ticket owners lose an average of $0.95 per raffle ticket.

• Each ticket owner will lose $0.95 per raffle ticket.

• A ticket owner would have to purchase 19 more tickets for the expected value of his or her net gain to increase to $0.00.

• A ticket owner has a 95 percent chance of having a ticket that is not selected.

The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of games are won, the player wins a prize. If the possible choices for n are n=10, n = 20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?

• n = 10

• n = 20

• n = 100

• n = 10 or n = 20, the probabilities are the same

• n = 10, n = 20, or n = 100; the probabilities are the same

The weight of tomatoes chosen at random from a bin at a farmer's market are Normally distributed with a mean of 10 ounces and standard deviation of 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is

• Normal with mean 10 ounces and standard deviation 1 ounce

• Normal with mean 40 ounces and standard deviation 2 ounces

• Normal with mean 40 ounces and standard deviation 4 ounces

• binomial, with mean 40 ounces and standard deviation 2 ounces

• binomial, with mean 40 ounces and standard deviation 4 ounces

Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital's capacity will be exceeded.

• 0.011

• 0.035

• 0.092

• 0.965

• 0.989

A psychologist studied the number of puzzles that subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a randomly chosen subject. The psychologist found that X has the given probability distribution. What is the probability that a randomly chosen completes more than the expected number of puzzles in the five-minute period while listening to soothing music?

• 0.1

• 0.4

• 0.8

• 1

• Cannot be determined

A psychologist studied the number of puzzles that subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a randomly chosen subject. The psychologist found that X has the given probability distribution. The standard deviation of X is 0.9. Which of the following is the best interpretation of this value?

• About 90% of the subjects solved 3 or fewer puzzles

• About 68% of subjects solved between 0.9 puzzles less and 0.9 puzzles more than mean

• The typical subject solved an average of 0.9 puzzles

• The number of puzzles solved by subjects typically differed from the mean by about 0.9 puzzles

• The number of puzzles solved by subjects typically differed from one another by 0.9 puzzles

A psychologist studied the number of puzzles that subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a randomly chosen subject. The psychologist found that X has the given probability distribution. The standard deviation of X is 0.9. Let D be the difference in the number of puzzles solved by two randomly selected subjects in a five-minute period. What is the standard deviation of D?

• 0

• 0.81

• 0.9

• 1.27

• 1.8

Assuming adult male heights are normally distribution with a mean of 70 inches and a standard deviation of 3 inches and female heights are normally distributed with a mean of 64 inches and standard deviation of 2 inches, which of the following would be the mean and standard deviation of the difference between male and female heights?

• mean = 67, sd = 62

• mean = 6, sd = 1

• mean = 6, sd = 3.6

• mean = 6, sd = 5

• mean = 6, sd = 13

A random sample of two observations is taken from a population that is normally distributed with a mean of 100 and a standard deviation of 5. What is the probability that the sum of the two observations is greater than 221?

• 0.0015

• 0.250

• 0.0500

• 0.4500

• 0.9985