Question 1181223: The random variable x represents the number of credit cards that adults have along with the corresponding probabilities. Find the mean and standard deviation.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! You haven't provided the data (the number of credit cards adults have and their corresponding probabilities). I need that information to calculate the mean and standard deviation. However, I can give you the formulas and explain the process.
**Let's say you have the following data (replace these with your actual data):**
| Number of Credit Cards (x) | Probability P(x) |
|---|---|
| 0 | 0.10 |
| 1 | 0.35 |
| 2 | 0.30 |
| 3 | 0.20 |
| 4 | 0.05 |
**1. Calculate the Mean (μ):**
The mean (or expected value) is calculated as:
μ = Σ [x * P(x)]
This means you multiply each value of x by its corresponding probability and then add up all those products.
Using our example data:
μ = (0 * 0.10) + (1 * 0.35) + (2 * 0.30) + (3 * 0.20) + (4 * 0.05)
μ = 0 + 0.35 + 0.60 + 0.60 + 0.20
μ = 1.75
**2. Calculate the Variance (σ²):**
The variance is calculated as:
σ² = Σ [(x - μ)² * P(x)]
This means you subtract the mean from each value of x, square the result, multiply by the corresponding probability, and then add up all those products.
Using our example data:
σ² = (0 - 1.75)² * 0.10 + (1 - 1.75)² * 0.35 + (2 - 1.75)² * 0.30 + (3 - 1.75)² * 0.20 + (4 - 1.75)² * 0.05
σ² = 3.0625 * 0.10 + 0.5625 * 0.35 + 0.0625 * 0.30 + 1.5625 * 0.20 + 5.0625 * 0.05
σ² = 0.30625 + 0.196875 + 0.01875 + 0.3125 + 0.253125
σ² = 1.0875
**3. Calculate the Standard Deviation (σ):**
The standard deviation is simply the square root of the variance:
σ = √σ²
Using our example data:
σ = √1.0875
σ ≈ 1.04
**Provide your data, and I'll calculate the mean and standard deviation for you.**
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