Find the mean and standard deviation of the given probability distribution.  Round your answers to 2 places after the decimal point, if necessary.
x
P (x)
0
0.05
4
0.24
5
0.32
7
0.16
8
0.23
Mean =   
Standard deviation =   


To find the mean and standard deviation of the given probability distribution, we use the following formulas:

1. **Mean (μ):**
\[
\mu = \sum [x \cdot P(x)]
\]
Where \( x \) is the value and \( P(x) \) is the probability of that value.

2. **Variance (σ²):**
\[
\sigma^2 = \sum [(x - \mu)^2 \cdot P(x)]
\]
3. **Standard Deviation (σ):**
\[
\sigma = \sqrt{\sigma^2}
\]

### Step 1: Calculate the mean (μ)
\[
\mu = (0 \times 0.05) + (4 \times 0.24) + (5 \times 0.32) + (7 \times 0.16) + (8 \times 0.23)
\]
I'll calculate that first.

### Step 2: Calculate the variance (σ²) after finding the mean.

Let me calculate these.### Mean (μ):
The mean of the given probability distribution is approximately 5.52.

### Standard Deviation (σ):
The standard deviation of the given probability distribution is approximately 1.98.

Would you like more details on any of the steps? Here are five related questions to deepen your understanding:

1. How is the variance related to standard deviation?
2. What does the standard deviation tell us about a distribution?
3. How would the mean change if we altered one of the probabilities?
4. Can you compute the variance directly without finding the mean first?
5. How does a discrete probability distribution differ from a continuous one?

**Tip:** When the standard deviation is low, the data points are close to the mean, indicating less variability in the distribution.

Find the mean and standard deviation of the given probability distribution. Round your answers to 2 places after the decimal point, if necessary.
x
P(x)
0: 0.05
4: 0.24
5: 0.32
7: 0.16
8: 0.23
Mean = 
Standard deviation = 

Learn how to calculate the mean and standard deviation of a probability distribution with the values 0, 4, 5, 7, and 8. This tutorial explains how to use the formulas for mean and standard deviation, rounding to two decimal places. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation