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, PX(x)?
To determine the probability distribution, PX(x), we need to find the probability of each possible value of the random variable X.
From the given information, we know the following:
- 50% of the students surveyed own 2 pets.
- 3 students own 3 pets each.
- 2 students own 4 pets each.
- 8 students own 1 pet.
Let's break down the probabilities for each value of X:
For X = 1:
We know that 8 students own 1 pet. Therefore, the probability of X = 1 is 8 divided by the total number of students surveyed.
For X = 2:
Given that 50% of the students surveyed own 2 pets, the probability of X = 2 is 0.50.
For X = 3:
We are told that 3 students own 3 pets each. Hence, the probability of X = 3 is 3 divided by the total number of students surveyed.
For X = 4:
According to the information, 2 students own 4 pets each. Therefore, the probability of X = 4 is 2 divided by the total number of students surveyed.
For all other values of X, the probability is 0 because there are no such cases mentioned.
To summarize, the probability distribution, PX(x), is as follows:
PX(1) = 8/(Total number of students surveyed)
PX(2) = 0.50
PX(3) = 3/(Total number of students surveyed)
PX(4) = 2/(Total number of students surveyed)
PX(x) = 0 for all other values of x.
To determine the probability distribution PX(x), we need to find the probability for each possible value of the random variable X.
Given the information provided, we can summarize the data as:
- 50% of students surveyed own 2 pets.
- 3 students own 3 pets each.
- 2 students own 4 pets each.
- 8 students own 1 pet.
Let's calculate the probability distribution PX(x) for each possible number of pets:
- P(X = 1) = 8/total surveyed students
- P(X = 2) = 50/total surveyed students
- P(X = 3) = 3/total surveyed students
- P(X = 4) = 2/total surveyed students
Note that the probability of each outcome can be found by dividing the count of students with that number of pets by the total number of students surveyed.
Since we don't know the total number of students surveyed, we cannot calculate the actual probabilities. However, we can express the probability distribution PX(x) based on the given data as follows:
PX(1) = 8/total surveyed students
PX(2) = 50/total surveyed students
PX(3) = 3/total surveyed students
PX(4) = 2/total surveyed students
Therefore, the probability distribution PX(x) for the given information is:
PX(1) = 8/total surveyed students
PX(2) = 50/total surveyed students
PX(3) = 3/total surveyed students
PX(4) = 2/total surveyed students