taylor surveys students in one grade level who own at least one pet. she finds that 50% of the students…

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, $p_x(x)$? probability distribution probability distribution

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, $p_x(x)$? probability distribution probability distribution

Answer

Explanation:

Step1: Calculate total number of students

Let the total number of students be $n$. We know that 8 students own 1 - pet, 3 students own 3 - pets each, 2 students own 4 - pets each, and 50% of $n$ own 2 - pets. So the number of students who own 2 - pets is $0.5n$. Then $n=8 + 3+2+0.5n$. Rearranging gives $n-0.5n=8 + 3+2$, so $0.5n = 13$ and $n = 26$.

Step2: Calculate probabilities for each value of $X$

For $x = 1$: $P(X = 1)=\frac{8}{26}\approx0.31$. For $x = 2$: Since 50% of students own 2 - pets, $P(X = 2)=0.5$. For $x = 3$: $P(X = 3)=\frac{3}{26}\approx0.12$. For $x = 4$: $P(X = 4)=\frac{2}{26}\approx0.08$.

Answer:

The probability - distribution bar chart with the correct heights for $x = 1,2,3,4$ corresponding to approximately $0.31,0.5,0.12,0.08$ respectively. (Since no specific options for bar - charts are given in text form, the above probabilities are the key values for the correct probability distribution).