AP Statistics 4.7 Introduction to Random Variables and Probability Distributions- MCQs - Exam Style Questions
▶️ Answer/Explanation
1. Identify Variable Types:
– The variable “type of animal” (Cat, Dog) is categorical.
– The variable “weight classification” (Healthy, Underweight, Overweight) is also categorical.
2. Select the Appropriate Graph:
– We need a graph that shows a relationship between two categorical variables.
– Stemplots, scatterplots, boxplots, and dotplots are used for quantitative (numerical) data.
– A segmented bar chart is specifically used to compare the proportions of a categorical variable across different groups.
This makes it the best choice to see if the proportion of healthy, underweight, and overweight animals differs between cats and dogs.
✅ Answer: (D)
▶️ Answer/Explanation
1. Find \(P(E)\) using the independence rule:
For independent events, \(P(D \text{ and } E) = P(D) \times P(E)\).
\(0.18 = 0.6 \times P(E)\)
\(P(E) = \frac{0.18}{0.6} = 0.3\)
2. Calculate \(P(D \text{ or } E)\) using the general addition rule:
\(P(D \text{ or } E) = P(D) + P(E) – P(D \text{ and } E)\)
\(P(D \text{ or } E) = 0.6 + 0.3 – 0.18\)
\(P(D \text{ or } E) = 0.9 – 0.18 = 0.72\)
✅ Answer: (D)