## Math Problem Statement

An agency collects demographics concerning the number of people in families per household in a certain country. Assume the distribution of the number of people per household is as shown in the table to the right.

a. nbspa.

Calculate the expected number of people in families per household in the country.

b.

Compute the standard deviation of the number of people in families per household.

nbsp nbsp

**x**

P(x)

nbsp nbsp 22

0.270.27

33

0.250.25

44

0.290.29

55

0.140.14

66

0.030.03

77

0.020.02

Question content area bottom

Part 1

a. The expected number of people in families per household is

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## Solution

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## Math Problem Analysis

### Mathematical Concepts

Probability

Expected Value

Standard Deviation

### Formulas

Expected value formula: E(X) = Σ[x * P(x)]

Standard deviation formula: σ = sqrt(E(X²) - [E(X)]²)

### Theorems

Law of Large Numbers

Properties of Expectation

### Suitable Grade Level

Grades 10-12

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