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WGU Applied-Probability-and-Statistics Exam Syllabus Topics:

Section	Objectives
Topic 1: Statistical Inference	- Hypothesis Testing (Introductory Level) 1. Null vs alternative hypothesis 2. p-values interpretation - Estimation and Confidence Intervals 1. Confidence interval interpretation 2. Point estimates
Topic 2: Probability Theory	- Probability Distributions 1. Normal distribution 2. Binomial distribution basics - Fundamental Probability Concepts 1. Conditional probability 2. Independent vs dependent events 3. Basic probability rules
Topic 3: Regression and Modeling	- Linear Relationships 1. Slope and intercept interpretation 2. Simple linear regression
Topic 4: Descriptive Statistics	- Single Variable Data Analysis 1. Data visualization (histograms, box plots) 2. Measures of central tendency (mean, median, mode) 3. Measures of dispersion (variance, standard deviation, range) - Two Variable Data Analysis 1. Scatter plots interpretation 2. Correlation 3. Outliers and relationships

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WGU Applied Probability and Statistics (FZO1 C955) Sample Questions (Q142-Q147):

NEW QUESTION # 142
A school surveyed student participation in extracurricular activities. The survey found:
* The drama club had 50% of students participate.
* The science club had 30% of students participate.
* Both clubs had 15% of students participate.
What is the probability that a student participated in the drama club, given that they attended the science club?

A. .40
B. .5
C. .3
D. .15

Answer: B

Explanation:
This question asks for a conditional probability. The phrase "given that they attended the science club" means the science club group becomes the restricted reference group. The required probability is P(drama club | science club), which is calculated as P(drama and science) divided by P(science). The problem states that 15% of students participated in both clubs, so P(drama and science) = 0.15. It also states that 30% participated in the science club, so P(science) = 0.30. Therefore, P(drama | science) = 0.15 ÷ 0.30 = 0.50. This means that among students who attended the science club, half also participated in drama club. Option A gives the joint probability, not the conditional probability. Option B gives only the science club participation rate. Option C does not match the conditional probability calculation. References/topics from the Study Guide: conditional probability, joint probability, probability ratios, two-event probability.

NEW QUESTION # 143
A study recorded the number of hours participants spent on exercise per week: 3 participants exercised for 1 hour, 6 participants exercised for 2 hours, 4 participants exercised for 3 hours, and 2 participants exercised for
4 hours.
Which type of graph would best represent the frequency of exercise hours?

A. A scatterplot with points showing the relationship between exercise hours and fitness level
B. A line graph with points connected to illustrate changes in exercise hours over time
C. A pie chart with slices representing the proportion of each exercise duration
D. A bar chart with bars showing the number of participants for each exercise duration

Answer: D

Explanation:
The data describe frequencies for a single variable: weekly exercise duration. Each duration, 1 hour through 4 hours, has an associated count of participants. A bar chart is the most appropriate display because it uses separate bars to show how many observations fall into each category or discrete value. Here, the bar above 1 hour would have height 3, the bar above 2 hours would have height 6, the bar above 3 hours would have height 4, and the bar above 4 hours would have height 2. A line graph is inappropriate because the data are not measuring change over time. A pie chart could show proportions, but the question specifically asks for frequency of exercise hours, making a bar chart clearer and more direct. A scatterplot requires two quantitative variables and is used to study association, not a one-variable frequency distribution. References
/topics from the Study Guide: frequency distributions, bar charts, single-variable data displays, quantitative
/discrete data.

NEW QUESTION # 144
Two mutually exclusive events: P(A and B) = ?

A. P(A) × P(B)
B. 0
C. 1
D. P(A) + P(B)

Answer: B

Explanation:
Mutually exclusive events cannot occur at the same time. If event A occurs, event B cannot occur, and if event B occurs, event A cannot occur. Therefore, the probability of both events occurring together is zero: P (A and B) = 0. For example, when rolling one die, the event "roll a 2" and the event "roll a 5" are mutually exclusive because one roll cannot produce both outcomes simultaneously. Option B applies to independent events, not mutually exclusive events. In fact, mutually exclusive events with positive probabilities are not independent because the occurrence of one eliminates the possibility of the other. Option C is part of the addition rule for mutually exclusive events when calculating P(A or B), not P(A and B). Option D would mean both events always occur together, which contradicts mutual exclusivity. Study Guide references/topics:
mutually exclusive events, joint probability, addition rule, probability foundations.

NEW QUESTION # 145
A fitness center owner notices that gym attendance increases as the number of daylight hours increases. The owner calculates a correlation coefficient between daylight hours and gym attendance of r = 0.72.
Based on this information, what can be concluded?

A. There is a positive, causal relationship between daylight hours and gym attendance.
B. There is a negative, causal relationship between daylight hours and gym attendance.
C. There is a positive association between daylight hours and gym attendance.
D. There is a negative association between daylight hours and gym attendance.

Answer: C

Explanation:
The correlation coefficient r measures the direction and strength of a linear association between two quantitative variables. Since r = 0.72 is positive, the relationship is positive: as daylight hours increase, gym attendance tends to increase. The value 0.72 also indicates a moderately strong to strong linear association because it is closer to 1 than to 0. However, correlation alone does not establish causation. Even though daylight hours and gym attendance move together, other variables could influence attendance, such as weather, seasonal routines, work schedules, or fitness promotions. Therefore, the valid conclusion is that there is a positive association, not a proven causal relationship. Options A and B are incorrect because they describe a negative relationship, which conflicts with the positive correlation coefficient. Option D overstates the evidence by claiming causation. References/topics from the Study Guide: correlation coefficient, positive association, linear relationship, correlation versus causation.

NEW QUESTION # 146
Expected value of binomial X ~ B(10, 0.3) = ?

A. 0
B. 1
C. 2
D. 0.3

Answer: C

Explanation:
For a binomial random variable, the expected value is E(X) = np, where n is the number of trials and p is the probability of success on each trial. In this problem, X ~ B(10, 0.3), so n = 10 and p = 0.3. Substituting into the formula gives E(X) = 10 × 0.3 = 3. This means that across many repetitions of the same binomial experiment, the average number of successes would be 3. Option B, 7, would correspond to the expected number of failures if the failure probability is 0.7. Option C gives only the number of trials, not the expected successes. Option D gives only the success probability, not the expected count. The expected value combines both trial count and success probability. Study Guide references/topics: binomial distribution, expected value, success probability, discrete random variables.

NEW QUESTION # 147
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