Complete the following probability distribution table: P(X) -2 0.26 44 62 0.14 80 0.24 88 0.26
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![**Educational Content on Probability Distribution Tables**
In this section, we are going to explore how to complete a probability distribution table. Below is an example of a probability distribution table that needs completion:
| X | P(X) |
|----|------|
| -2 | 0.26 |
| 44 | |
| 62 | 0.14 |
| 80 | 0.24 |
| 88 | 0.26 |
**Explanation:**
- **Column X** represents the values of the random variable.
- **Column P(X)** represents the probabilities associated with each of these values.
**Objective:**
The goal is to find the missing probability for the value \( X = 44 \).
**Steps to Complete the Table:**
1. **Understand that the sum of probabilities must equal 1:**
In any probability distribution, the total of the probabilities must always add up to 1.
2. **Calculate the missing probability:**
To find the missing probability P(44), add up all given probabilities and subtract from 1:
\[
0.26 + 0.14 + 0.24 + 0.26 = 0.90
\]
\[
1 - 0.90 = 0.10
\]
3. **Fill in the missing probability:**
Now that we've computed that P(44) = 0.10, the completed table should look like this:
| X | P(X) |
|----|------|
| -2 | 0.26 |
| 44 | 0.10 |
| 62 | 0.14 |
| 80 | 0.24 |
| 88 | 0.26 |
Having a complete probability distribution table is essential for analyzing the likelihood of different outcomes in a probabilistic scenario.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d201130-f4f7-4c89-8a7d-8eb0f7158013%2F5a06de35-2283-4b5e-a080-bcbbc6419b36%2F5t3v4xp_processed.jpeg&w=3840&q=75)
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