A particular company pays its employees an average daily rate of $120 with a standard deviation of $12.

A group of 3,000 people had participated in a field trip. Using the Empirical Rule determine about how many of them should have a daily pay of more than $144?

The number of people that have a daily rate of more than 144 is  .

*(note: this question is asking for the number of people, not the percentage of people)*

Given:
- Mean daily rate (μ) = $120
- Standard deviation (σ) = $12
- Group size = 3,000 people

We need to determine how many of these people have a daily pay of more than $144.

### Step 1: Calculate the Z-score
First, find how many standard deviations $144 is above the mean:
\[
Z = \frac{144 - 120}{12} = \frac{24}{12} = 2
\]
So, $144 is 2 standard deviations above the mean.

### Step 2: Use the Empirical Rule
According to the Empirical Rule:
- About 95% of the data falls within 2 standard deviations (between $96 and $144).
- This means that 5% of the data falls outside this range, with 2.5% below $96 and 2.5% above $144.

### Step 3: Calculate the number of people
Since 2.5% of the people earn more than $144 per day:
\[
\text{Number of people} = 0.025 \times 3000 = 75
\]

Final answer:
The number of people that have a daily rate of more than $144 is **75**.

Do you want more details or have any questions?

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Here are some related questions:

1. How many people earn less than $96 per day?
2. What is the probability that a randomly selected employee earns between $108 and $132?
3. How many people earn between $120 and $144 per day?
4. What percentage of employees earn between $96 and $144 per day?
5. How would the answer change if the group size were 6,000 people?
6. What are the limitations of using the Empirical Rule for this kind of analysis?
7. How can the Z-score table be used to find the exact percentage?
8. What is the significance of being more than 2 standard deviations above the mean in this context?

**Tip:** The Empirical Rule is helpful for quick estimates, but the exact number can be found using a Z-score and cumulative distribution tables.

Explore how to estimate the distribution of daily pay using the Empirical Rule. Given a mean daily rate of $120 with a standard deviation of $12, determine how many people out of a group of 3,000 have a daily pay of more than $144. Learn the application of Z-score and the Empirical Rule in statistics.

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