Question 1208817
Here's how to calculate the necessary sample size:

**1. Identify Key Values:**

* **Confidence Level:** 99%
* **Margin of Error (E):** 2% = 0.02
* **Pilot Survey:** 8 out of 47 have two or more jobs.  This gives us a preliminary estimate of the proportion (p̂):  p̂ = 8/47 ≈ 0.1702

**2. Find the Z-score:**

For a 99% confidence level, the alpha (α) is 1 - 0.99 = 0.01.  Since it's a two-tailed test, we divide alpha by 2: 0.01 / 2 = 0.005.  We want the z-score that corresponds to an area of 0.995 (1 - 0.005) in the standard normal distribution table.

Z-score ≈ 2.58 (rounded to two decimal places).

**3. Use the Sample Size Formula:**

Since we have a preliminary estimate of the proportion from the pilot study, we use the following formula for sample size:

n = (Z² * p̂ * (1 - p̂)) / E²

Where:

* n = sample size
* Z = Z-score
* p̂ = estimated proportion
* E = margin of error

**4. Plug in the Values and Calculate:**

n = (2.58² * 0.1702 * (1 - 0.1702)) / 0.02²
n = (6.6564 * 0.1702 * 0.8298) / 0.0004
n = 0.9457 / 0.0004
n ≈ 2364.25

**5. Round Up:**

Always round the sample size *up* to the next whole number to ensure the desired confidence level and margin of error are met.

n = 2365

**Answer:**

You should interview 2365 people in the workforce to meet your requirements.