Question

taylor surveys students in one grade level who own at least one pet. she finds that 50% of the students surveyed own 2 pets, 3 students own 3 pets each, and 2 students own 4 pets each. eight of the students in the grade own 1 pet. considering the number of pets as the random variable, x, which of the following is the probability distribution, ( p_x(x) )?

Explanation:

Step1: Find total number of students

Let total students be \( n \). Students with 1 pet: 8, with 3 pets: 3, with 4 pets: 2, and with 2 pets: \( 0.5n \). So \( n = 8 + 0.5n + 3 + 2 \). Solve: \( n - 0.5n = 13 \) → \( 0.5n = 13 \) → \( n = 26 \).

Step2: Calculate probabilities

• \( P(1) = \frac{8}{26} \approx 0.307 \) (matches the first bar height ~0.3).
• \( P(2) = 0.5 \) (matches the second bar height ~0.5).
• \( P(3) = \frac{3}{26} \approx 0.115 \) (third bar ~0.1).
• \( P(4) = \frac{2}{26} \approx 0.077 \) (fourth bar ~0.08).

The first graph (top one) has these probabilities.

Answer:

The top Probability Distribution graph (with bars at x=1,2,3,4 matching the calculated probabilities).