The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts​ (a) through​ (c) below.Accidents_Daily_(X)	P(X=xi)

0	0.28

1	0.34

2	0.16

3	0.09

4	0.06

5	0.04

6	0.03 Compute the standard deviation.

​(Type an integer or a decimal. Do not​ round.)

To compute the standard deviation of a probability distribution, we follow these steps:

1. **Calculate the mean (μ)**:
\[
\mu = \sum X \cdot P(X)
\]
Where \(X\) represents the number of accidents and \(P(X)\) is the probability.

2. **Calculate the variance**:
\[
\sigma^2 = \sum (X - \mu)^2 \cdot P(X)
\]
Where \(X - \mu\) is the deviation from the mean for each \(X\), and \(P(X)\) is the probability.

3. **Take the square root of the variance** to get the standard deviation (σ):
\[
\sigma = \sqrt{\sigma^2}
\]

Let's begin by calculating the mean, then move on to the variance and standard deviation. I'll calculate that for you.1. **Mean (μ)**: \( 1.55 \)

2. **Variance (σ²)**: \( 2.4275 \)

3. **Standard deviation (σ)**: \( 1.558 \)

So, the standard deviation of the number of daily traffic accidents is approximately **1.558**.

Do you have any questions or would you like more details?

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Here are 5 related questions for further exploration:

1. What is the expected number of daily traffic accidents?
2. How would the standard deviation change if one probability value were different?
3. How is variance related to standard deviation?
4. What is the probability of having fewer than 3 accidents?
5. How would we compute the cumulative distribution for this scenario?

**Tip**: The standard deviation tells us how much the number of accidents deviates from the mean on average.

The following table contains the probability distribution for the number of traffic accidents daily in a small town. Complete parts (a) through (c) below. Accidents Daily (X) P(X=xi) 0 0.28 1 0.34 2 0.16 3 0.09 4 0.06 5 0.04 6 0.03 Compute the standard deviation. (Type an integer or a decimal. Do not round.)

Learn how to compute the standard deviation of a probability distribution for daily traffic accidents in a small town. The step-by-step solution covers calculating the mean, variance, and standard deviation. Suitable for students in Grades 10-12.

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