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.