AP Stats - 4.1-4.2 Practice

An online customer service department estimates that about 15 percent of callers have to wait more than 8 minutes to have their calls answered by a person. The department conducted a simulation of 1,000 trials to estimate the probabilities that a certain number of callers out of the next 10 callers will have to wait more than 8 minutes to have their calls answered. The simulation is shown in the following histogram. Based on the simulation, what is the probability that at most 2 of the next 10 callers will have to wait more than 8 minutes to have their calls answered?

• 0.150

• 0.190

• 0.474

• 0.526

• 0.810

Mateo plays on his school basketball team. From past history, he knows that his probability of making a basket on a free throw is 0.8. Suppose he wants to create a simulation using random numbers to estimate the probability of making at least 3 baskets on his next 5 free throw attempts. Which of the following assignments of the digits 0 to 9 could be used for the simulation?

• Let the even digits represent making a basket and the odd digits represent not making a basket.

• Let the digits 0 and 1 represent making a basket and the digits from 2 to 9 represent not making a basket.

• Let the digits from 0 to 3 represent making a basket and the digits from 4 to 9 represent not making a basket.

• Let the digits from 0 to 6 represent making a basket and the digits from 7 to 9 represent not making a basket.

• Let the digits from 0 to 7 represent making a basket and the digits 8 and 9 represent not making a basket.

Joslyn performed an experiment using a die with its faces numbered from 1 to 6. She rolled the die and recorded whether the 5 landed face up. She repeated the process many times and kept a cumulative record of the total number of rolls and the total number of 5s landing face up. The following table shows part of her record.Suppose Joslyn could roll the die 10,000 times and keep a record of the total number of 5s landing face up in the 10,000 rolls. What would such a record illustrate?

• The conditional probability rule

• The multiplication rule

• The addition rule

• The law of large numbers

• The property of mutually exclusive events

At a sporting event, cheerleaders will throw 50 bundled T-shirts into the crowd. The T-shirt sizes consist of 10 small, 15 medium, and the remainder either large or extra large. Suppose Ana catches a T-shirt. What is the probability that she will catch a T-shirt that is not a size small?

• 0.10

• 0.20

• 0.50

• 0.67

• 0.80

A middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two students from the club will be selected at random to participate in the county chess tournament. What is the probability that Adam and Ella will be selected?

• 1/20

• 1/10

• 1/8

• 1/7

• 1/4

A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3 ?

• For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/3.

• For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/2.

• For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 2/3.

• For three rolls of the die, a number less than 3 will land face up one time.

• It will take three rolls of the die before a number less than 3 lands face up for the first time.

A store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is 0.68.

• For all customers who purchase a lawn mower, 68% will also purchase an extended warranty.

• For all customers of the store, 68% will purchase a lawn mower.

• For all customers who purchase an extended warranty, 68% will use the warranty.

• From the next 25 customers, 17 will purchase an extended warranty.

• From the next 25 customers, 17 will purchase a lawn mower.

The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. Is Avery interpreting the probability correctly?

• Yes, because 2 out of 5 is equal to 40%.

• Yes, because participants in the survey are selected at random.

• Yes, because participants in the survey are selected at random.

• No, because only 40% of all people will visit the site.

• No, because 0.40 represents probability in the long run over many visits to the site.

In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. One car will be selected at random from the parking lot. If each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green?

• 0

• 0.1

• 0.2

• 0.5

• 0.6

A high school science teacher has 78 students. Of those students, 35 are in the band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One student from the 78 students will be selected at random. Let event B represent the event of selecting a student in the band, and let event S represent the event of selecting a student on a sports team.

Are B and S mutually exclusive events?

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