Chapter 10 AP Statistics

Which of the following is a true statement?

• The binomial setting requires that there are only two possible outcomes for each trial, while the geometric setting permits more than two outcomes.

• A geometric random variable takes on integer values from 0 to n.

• If X is a geometric random variable and the probability of success is 0.85, then the probability distribution of X will be skewed left, since 0.85 is closer to 1 than to 0.

• There is a fixed number of trials in a geometric setting, and the number of trials varies in a binomial setting.

• The distribution of every geometric random variable is skewed right

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately Normal with mean $360 and standard deviation $50. The least profitable 10% of days have a profit of at most how many dollars?

• $244

• $296

• $370

• $424

• $476

A spinner has 5 equally-sized regions (blue, green, red, orange, and yellow). If you spin the spinner 20 times, what is the probability that the spinner lands on blue at most 5 times?

• Approximately 0

• 0.370

• 0.630

• 0.804

• Approximately 1

Which of the following random variables is discrete?

• The number of shots made in 10 free-throw attempts.

• The weight of a rhinoceros.

• The species of an insect.

• The length of a needle on a saguaro cactus.

• None of the variables above are discrete.

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the given distribution. The expected value of X is E(X) =

• 0.40

• 1.00

• 1.45

• 1.66

• 2.50

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the given distribution. The standard deviation of X is 1.27. Interpret this value.

• The number of computers in a randomly selected household is within 1.27 of the mean.

• The number of computers in a randomly selected household is exactly 1.27 from the mean.

• The number of computers in a randomly selected household is 1.27, on average.

• The number of computers in a randomly selected household is typically 1.27 from the mean.

• The average number of computers in a randomly selected household is typically 1.27 from the mean.

A marketing survey compiled data on the number of personal computers in households. X = the number of computers in a randomly-selected household. If you were to randomly select households, what is the probability it would take exactly 8 selections to find one with 5 computers?

• Approximately 0

• 0.02

• 0.03

• 0.32

• Approximately 1

The number of DVDs rented daily at DVD rental machine has a mean of 134 with a standard deviation of 32. Select two days at random and find the difference in the number of DVDs rented on the two days. What are the mean and standard deviation of the difference in the number of DVDs rented?

• Mean = 0, Standard Deviation = 0

• Mean = 0, Standard Deviation = 64

• Mean = 0, Standard Deviation = 45

• Mean = 92, Standard Deviation = 32

• Mean = 134, Standard Deviation = 32

The number of DVDs rented daily at DVD rental machine has a mean of 134 with a standard deviation of 32. The cost of the electricity to keep the DVD rental machine on is $1.45 per day. Each DVD rental increases the electricity cost by $0.02. What are the mean and standard deviation of the electricity cost per day?

• Mean = $4.13, Standard Deviation = $0.64

• Mean = $4.13, Standard Deviation = $1.77

• Mean = $4.13, Standard Deviation = $2.09

• Mean = $2.68, Standard Deviation = $0.64

• Mean = $2.68, Standard Deviation = $2.09

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

• 0.965

• 0.035

• 0.989

• 0.092