The problem in the image involves using the normal approximation to estimate probabilities based on a binomial distribution. Here's a breakdown of the problem you're working on:

1. Part 1 of 6:

   • Question: Is it appropriate to use the normal approximation to find the probability that less than 8.4% of the sample holds multiple jobs?
   • Reasoning: The normal approximation is appropriate if $np \geq 10$ and $n(1-p) \geq 10$. Here, $p = 0.12$, and $n = 245$, so: $np = 245 \times 0.12 = 29.4 \quad \text{and} \quad n(1-p) = 245 \times 0.88 = 215.6.$ Both values are greater than 10, so the normal approximation is appropriate.

2. Part 2 of 6:

   • Question: Find the probability that less than 8.4% of individuals in a sample of 245 hold multiple jobs.
   • Answer: The probability is given as $0.0418$.

3. Part 3 of 6:

   • Question: For a new sample of 333 employed adults, find the probability that less than 8.4% of individuals hold multiple jobs.
   • Answer: The probability for this new sample is $0.0217$.

4. Part 4 of 6:

   • Question: Find the probability that more than 7.9% of individuals in the sample of 333 hold multiple jobs.
   • Process: You'll use the normal approximation to find this probability. You need to calculate the mean and standard deviation of the binomial distribution first and then apply the z-score formula for a cumulative normal distribution.

Would you like a detailed solution for Part 4, including the calculations for the probability?

Here are five follow-up questions you could explore based on this scenario:

1. How do you calculate the z-score for the normal approximation in Part 4?
2. Why is the normal approximation valid in these scenarios, and when might it not be valid?
3. What is the effect of increasing the sample size on the probability estimates?
4. How does changing the percentage (e.g., from 8.4% to 7.9%) affect the probability?
5. Could a different distribution be used instead of the normal approximation, and why?

Tip: Always check if the conditions for using the normal approximation are satisfied before applying it.