AP Stats Unit

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

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

In a binomial distribution with n = 9, p = 0.52. Find the mean and standard deviation.

• mean = 1.50, sd = 4.32

• mean = 4.68, sd = 1.50

• mean = 2.16, sd = 2.25

• mean = 4.32, sd = 1.50

• mean = 4.32, sd = 2.25

Which of these variables is binomial?

• time it takes to attempt 10 independent free throws

• time it takes to make 10 independent free throws

• number of shots made in 10 independent attempts at free throws

• number of attempts to make 10 independent free throws

• none of these

A college basketball player makes 80% of her free throws. Suppose this probability is the same for each free throw she attempts, and free throw attempts are independent. The expected number of free throws required until she makes her first free throw of the season is

• 2

• 1.25

• 0.80

• 0.31

• 0.13

Suppose that 40% of the cars in a certain town are white. A person stands at an intersection waiting for a white car. Let X = the number of cars that must drive by until a white one drives by. P(X < 5) =

• 0.0518

• 0.1296

• 0.2592

• 0.8704

• 0.9482

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

A random sample of households is taken. For each household, the number of hours spent watching television and the power consumption (in kWh) during a day are recorded. The table below shows computer output from a linear regression analysis on the data. Which of the following is the equation of the least-squares regression line?

• ŷ = 19.31 + 0.891x

• ŷ = 2.8621 + 0.2715x

• ŷ = 0.891 + 19.31x

• ŷ = 0.2715 + 2.8621x

• ŷ = 0.2715 + 0.891x

A random sample of households is taken. For each household, the number of hours spent watching television and the power consumption (in kWh) during a day are recorded. The table below shows computer output from a linear regression analysis on the data. Which of the following is a correct interpretation of r²?

• Number of hours of television explains 30% of the variability in power consumption.

• 30% of the increase in number of hours of television is explained by power consumption.

• 30% of the data will lie on the least-squares regression line.

• 30% of the residuals will be less than 4.185.

• All of the above are correct interpretations.