Construct the probability distribution based on the following frequency distribution: OUTCOMES: 102, 105 108 ,111,

To construct a probability distribution from a given frequency distribution, we first need to understand the concept of frequency and how it relates to probability. The frequency distribution provides us with the counts of occurrences for each outcome, while the probability distribution gives us the likelihood of each outcome occurring, expressed as a fraction of the total occurrences.

Step-by-Step Construction of the Probability Distribution

Let's break this down into manageable steps. Assume we have the following frequency distribution for the outcomes 102, 105, 108, and 111:

• Outcome 102: Frequency = 5
• Outcome 105: Frequency = 10
• Outcome 108: Frequency = 15
• Outcome 111: Frequency = 20

Now, we will follow these steps to create the probability distribution:

1. Calculate the Total Frequency

The first step is to sum up all the frequencies:

Total Frequency = 5 + 10 + 15 + 20 = 50

2. Calculate the Probability for Each Outcome

Next, we find the probability of each outcome by dividing the frequency of each outcome by the total frequency:

• Probability of 102 = Frequency of 102 / Total Frequency = 5 / 50 = 0.1
• Probability of 105 = Frequency of 105 / Total Frequency = 10 / 50 = 0.2
• Probability of 108 = Frequency of 108 / Total Frequency = 15 / 50 = 0.3
• Probability of 111 = Frequency of 111 / Total Frequency = 20 / 50 = 0.4

3. Compile the Probability Distribution

Now that we have the probabilities, we can compile them into a probability distribution table:

Understanding the Probability Distribution

This probability distribution tells us how likely each outcome is to occur. For instance, the outcome 111 has the highest probability of 0.4, meaning it is the most likely to happen, while the outcome 102 is the least likely with a probability of 0.1. The sum of all probabilities should equal 1, which in this case is:

0.1 + 0.2 + 0.3 + 0.4 = 1.0

This confirms that our calculations are correct. Probability distributions are essential in statistics as they help us understand the behavior of random variables and make informed predictions based on observed data.