Statistics Test: Advanced Placement! Trivia Questions Quiz

1. Random variable X is normally distributed, with a mean of 25 and a standard deviation of 4. Which of the following is the approximate interquartile range for this distribution?

25.00 - 22.30 = 2.70

27.70 - 22.30 = 5.40

27.70 / 22.30 = 1.24

2.00(4.00) = 8.00

37.00 - 13.00 = 24.00

The interquartile range is a measure of the spread of data and is calculated as the difference between the upper quartile and the lower quartile. In this case, the upper quartile is approximately 27.70 and the lower quartile is approximately 22.30. Therefore, the approximate interquartile range is 27.70 - 22.30 = 5.40.

Explanation

The interquartile range is a measure of the spread of data and is calculated as the difference between the upper quartile and the lower quartile. In this case, the upper quartile is approximately 27.70 and the lower quartile is approximately 22.30. Therefore, the approximate interquartile range is 27.70 - 22.30 = 5.40.

2. An experiment was designed to test the effects of three different types of paint on the durability of wooden toys. Because boys and girls tend to play differently with toys, a randomly selected group of children was divided into two groups based on gender. Which of the following statements about this experiment is true?

There are three types of paint and two gender groups, giving a total of six treatment combinations in this experiment.

Type of paint is a blocking factor.

Gender is a blocking factor.

This is a completely randomized design.

This is a matched pairs design in which one boy and one girl are matched by age to form a pair.

In this experiment, the researchers divided the children into two groups based on gender. This means that gender is a factor that is being controlled for in the study. By doing so, the researchers can determine if there are any differences in the effects of the three types of paint on the durability of wooden toys between boys and girls. Therefore, the statement "Gender is a blocking factor" is true.

Explanation

In this experiment, the researchers divided the children into two groups based on gender. This means that gender is a factor that is being controlled for in the study. By doing so, the researchers can determine if there are any differences in the effects of the three types of paint on the durability of wooden toys between boys and girls. Therefore, the statement "Gender is a blocking factor" is true.

3. A medicine is known to produce side effects in one in five patients taking it. Suppose a doctor prescribes the medicine to four unrelated patients. What is the probability that none of the patients will develop side effects?

0.8000

0.4096

0.2500

0.2000

0.0016

The probability that none of the patients will develop side effects can be calculated using the formula for independent events. Since the medicine is known to produce side effects in one in five patients, the probability of a patient not developing side effects is 4/5. Since there are four unrelated patients, the probability that none of them will develop side effects is (4/5) * (4/5) * (4/5) * (4/5) = 0.4096.

Explanation

The probability that none of the patients will develop side effects can be calculated using the formula for independent events. Since the medicine is known to produce side effects in one in five patients, the probability of a patient not developing side effects is 4/5. Since there are four unrelated patients, the probability that none of them will develop side effects is (4/5) * (4/5) * (4/5) * (4/5) = 0.4096.

4. An insurance agent is successful in selling a life insurance policy to 20 percent of the customers she contacts. She decides to construct a simulation to estimate the mean number of customers she needs to contact before being able to sell a policy. Which of the following schemes should she use to do the simulation?

Assign numbers 0, 1 to successfully selling a policy to a customer and numbers 2, 3, 4 to failing to sell a policy to a customer.

Assign numbers 0, 1 to successfully selling a policy to a custome and numbers 2, 3, 4, 5, 6, 7, 8, 9 to failing to sell a policy to a customer.

Assign number 0 to successfully selling a policy to a customer and number 1 to failing to sell a policy to a customer.

Assign numbers 0, 1, 2, 3, 4 to successfully selling a policy to a customer and numbers 5, 6, 7, 8, 9, to failing to sell a policy to a customer.

Assign number 20 to successfully a policy to a customer and numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 to failing to sell a policy to a customer.

The insurance agent should use the scheme of assigning numbers 0, 1 to successfully selling a policy to a customer and numbers 2, 3, 4, 5, 6, 7, 8, 9 to failing to sell a policy to a customer. This scheme accurately represents the probability of success (20%) and failure (80%) in selling a policy. By using this scheme in the simulation, the agent can generate random numbers and simulate the process of contacting customers until a policy is sold. This will help estimate the mean number of customers she needs to contact before making a sale.

Explanation

The insurance agent should use the scheme of assigning numbers 0, 1 to successfully selling a policy to a customer and numbers 2, 3, 4, 5, 6, 7, 8, 9 to failing to sell a policy to a customer. This scheme accurately represents the probability of success (20%) and failure (80%) in selling a policy. By using this scheme in the simulation, the agent can generate random numbers and simulate the process of contacting customers until a policy is sold. This will help estimate the mean number of customers she needs to contact before making a sale.

5. Which of the following statements about any two events A and B is true?

P(A U B) = 0 implies events A and B are independent.

P(A U B) = 1 implies events A and B are mutually exclusive.

P(A ∩ B) = 0 implies events A and B are independent.

P(A ∩ B) = 0 implies events A and B are mutually exclusive.

P(A ∩ B) = P(A) - P(B) implies events A and B are equally likely events.

If the probability of the intersection of events A and B is 0, it means that there is no overlap between the two events. This implies that the occurrence of one event does not affect the occurrence of the other event, making them mutually exclusive. In other words, if event A happens, event B cannot happen, and vice versa. Therefore, the statement "P(A ∩ B) = 0 implies events A and B are mutually exclusive" is true.

Explanation

If the probability of the intersection of events A and B is 0, it means that there is no overlap between the two events. This implies that the occurrence of one event does not affect the occurrence of the other event, making them mutually exclusive. In other words, if event A happens, event B cannot happen, and vice versa. Therefore, the statement "P(A ∩ B) = 0 implies events A and B are mutually exclusive" is true.