Test on Introduction to Statistical Concepts and Methods

Question 1: The science of measuring uncertainty is known as probability.

A. Ano

B. Ne

Explanation: The study materials explicitly state: "The science of measuring ‘uncertainty’ is called probability."

Question 2: Which of the following statements correctly describe the application of addition rules in probability theory, based on the provided study materials?

A. The special rule of addition is applied when two events are independent, stating that P(A or B) = P(A) + P(B).

B. The general addition rule is used when events are not mutually exclusive, calculating P(A or B) as P(A) + P(B) - P(A and B).

C. If events are mutually exclusive, meaning they cannot occur simultaneously, the probability of either event A or event B occurring is P(A) + P(B).

D. Addition rules are primarily used to determine the probability of event A and event B both happening in two successive outcomes.

Explanation: The study materials state that the general addition rule applies when events are not mutually exclusive, using the formula P(A or B) = P(A) + P(B) - P(A and B) to avoid double counting. It also specifies that the special rule of addition is used for mutually exclusive events, where P(A or B) = P(A) + P(B). Option 0 is incorrect because the special rule applies to mutually exclusive events, not independent events. Option 3 is incorrect as addition rules are for 'one event or another occurring' (union), while multiplication rules are used for 'event A and event B both happen' (intersection).

Question 3: The multiplication rule of counting states that if there are m ways an event A can happen and n ways an event B can happen, then there are m plus n ways for both events to happen.

A. Ano

B. Ne

Explanation: The multiplication rule of counting states that if there are m ways in which event A can happen and n ways in which event B can happen, then there are m times n ways in which both can happen, not m plus n.

Question 4: A library has a new arrivals shelf with 12 popular books. A book club member wants to select 3 books to read from this shelf. If the order in which the books are chosen does not matter, how many different selections of books can be made?

A. 1320

B. 220

C. 36

D. 720

Explanation: The combination rule is used when the order of selection does not matter. In this problem, we are selecting 3 books from 12, and the order is not important. Using the combination rule nCx = n! / (x! * (n-x)!), with n=12 and x=3: 12C3 = 12! / (3! * (12-3)!) = 12! / (3! * 9!) = (12 * 11 * 10) / (3 * 2 * 1) = 1320 / 6 = 220.

Question 5: When finding the z-score for a given area, if the area falls to the left of the mean, the z-score will always be positive.

A. Ano

B. Ne

Explanation: If the area falls to the left of the mean, the z-score is negative. A positive z-score indicates the area falls to the right of the mean.