The mean income of households in a certain city is 25,000 dollars, with a standard deviation of 2,700.

Assuming a normal distribution, determine the probability that a randomly chosen household will have income less than 28,823 dollars.

The probability is:     %

*(Round your answer to the nearest whole percent)*

*(Omit the percent sign)*

To determine the probability that a randomly chosen household will have an income less than $28,823, we can use the z-score formula and refer to the standard normal distribution table.

### Step 1: Identify the mean and standard deviation
- Mean ($\mu$) = $25,000
- Standard deviation ($\sigma$) = $2,700

### Step 2: Calculate the z-score
The z-score formula is:
\[
z = \frac{X - \mu}{\sigma}
\]
Where:
- $X = 28,823$

Substituting the values:
\[
z = \frac{28,823 - 25,000}{2,700} = \frac{3,823}{2,700} \approx 1.4159
\]

### Step 3: Find the corresponding probability
Now, we look up the z-score of 1.4159 in the standard normal distribution table (or use a calculator or software).

A z-score of 1.4159 corresponds to a cumulative probability of approximately 0.921 (or 92.1%).

### Step 4: Express the probability as a percentage
The probability that a randomly chosen household will have an income less than $28,823 is approximately **92%**.

Would you like more details or have any questions?

### Related Questions
1. What is the probability of a household having an income greater than $20,000?
2. What percentage of households have incomes between $22,300 and $27,700?
3. How many households have incomes above $30,000 if there are 10,000 households in the city?
4. What is the income level at the 75th percentile?
5. How many households earn less than $23,000?
6. What is the probability that a household earns between $26,000 and $28,000?
7. What income value corresponds to the 95th percentile?
8. If a household earns $22,500, what is their z-score?

### Tip
When working with normal distributions, it's helpful to memorize common z-scores and their corresponding cumulative probabilities for quicker estimations.

Learn how to calculate the probability that a randomly chosen household will have an income less than $28,823 using the normal distribution and z-score. Given mean income of $25,000 and standard deviation of $2,700.

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