https://file.aiquickdraw.com/mathbot/file/1728861077746kr1fux9e.jpg

From the image you uploaded, it seems to be a problem set involving the use of the **Normal Approximation to the Binomial Distribution**. Let's go through each part to better understand and solve them:

### Part 1 of 5 (a):
- It asks whether it's appropriate to use the normal approximation.
  - The rule of thumb for using the normal approximation is:
    - \( np \geq 10 \) 
    - \( n(1-p) \geq 10 \)
  - In this case:
    - \( np = 7 \) (which is less than 10), so **it is not appropriate** to use the normal curve.

### Part 2 of 5 (b):
- You are given a new sample of 90 workers and asked to find the probability that more than 19% are government workers.
  - Based on the information in the image, this probability is **0.0853**.

### Part 3 of 5 (c):
- The task is to find the probability that the proportion of workers in the sample of 90 who are government employees is between 0.13 and 0.18.
  - The answer provided is **0.4707**.

### Part 4 of 5 (d):
- The question asks for the probability that less than 25% of the workers in the sample of 90 are government employees.
  - There is a placeholder in the image, and you would need to calculate this using the normal approximation or a similar method based on the binomial distribution.

Would you like help with further explanations or calculations for any of the parts? 

Here are five related questions for further practice:
1. How do you calculate the z-score for a given probability in a normal distribution?
2. Why is the rule of \( np \geq 10 \) important for normal approximations to binomial distributions?
3. How would you calculate the probability for part (d) step by step?
4. What is the difference between a cumulative normal probability and a single-point probability?
5. How do continuity corrections affect the normal approximation of binomial distributions?

**Tip:** Always check if both \( np \) and \( n(1-p) \) are greater than or equal to 10 before using the normal approximation for binomial problems.

The original question submitted by the user as text, regarding the use of normal approximation in binomial distribution for government employee sample proportions.

Explore how to apply the normal approximation to the binomial distribution for calculating probabilities involving government workers' proportions in a sample. Includes detailed solutions for cases with proportions like 0.19, 0.13, and 0.18. Learn key concepts such as z-scores and binomial distribution conditions.

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