STAT 200 ADVANCED PROBABILITY AND STATISTICS - WEEK 4 QUESTIONS AND ANSWERS

STAT 200 ADVANCED PROBABILITY
AND STATISTICS - WEEK 4 QUESTIONS
AND ANSWERS




1. A normal distribution has a mean of 100 and a standard deviation of 15. What is the z-score

for a value of 130?

A. 2.00


B. 1.50


C. 1.00


D. 2.50


Answer: A


Conceptual Explanation: The z-score is calculated as (X - mean) / standard deviation.

Here, (130 - 100) / 15 = = 2.00.


2. In a binomial distribution with n = 20 and p = 0.4, what is the expected value (mean)?

A. 6.0


B. 12.0


C. 4.8

,D. 8.0


Answer: D


Conceptual Explanation: The mean of a binomial distribution is E(X) = n * p. So, 20 * 0.4 =

8.0.


3. Which of the following is a necessary condition for a distribution to be considered a

discrete probability distribution?

A. The sum of all probabilities must be 1.


B. Each individual probability must be between -1 and 1.


C. The sum of all probabilities must be 0.


D. The probabilities must follow a bell-shaped curve.


Answer: A


Conceptual Explanation: For any discrete probability distribution, the sum of all

probabilities P(x) must equal 1 and each individual P(x) must be between 0 and 1.


4. Suppose P(A) = 0.3 and P(B) = 0.4. If events A and B are independent, what is P(A and B)?

A. 0.70


B. 0.10


C. 0.12


D. 0.50

, Answer: C


Conceptual Explanation: For independent events, P(A and B) = P(A) * P(B). Thus, 0.3 * 0.4

= 0.12.


5. Find the standard error of the mean for a population with a standard deviation of 20 and a

sample size of 100.

A. 0.2


B. 2.0


C. 5.0


D. 20.0


Answer: B


Conceptual Explanation: Standard Error (SE) = sigma / sqrt(n). So, 20 / sqrt(100) = 20 /

10 = 2.0.


6. What is the z-score such that the area to its left under the standard normal curve is 0.975?

A. 1.645


B. 2.33


C. 1.96


D. 2.58


Answer: C