From the image, it seems that you're working on a problem involving probability calculations based on proportions of government employees in a sample of 90 workers.

Here’s a breakdown of the results for each part shown in the image:

1. Part (b): The probability that more than 19% of the workers are government employees is given as 0.0853.

2. Part (c): The probability that the proportion of government workers is between 0.13 and 0.18 is 0.4707.

3. Part (d): The probability that less than 25% of the workers are government employees is 0.9981.

4. Part (e): The question asks whether it would be unusual if the proportion of government employees is greater than 0.25, with an option to select the probability.

Do you want help with any specific part of this, or would you like detailed explanations on the steps involved in solving these problems?

Relative Questions:

1. How is the normal distribution used in finding probabilities of proportions?
2. What is the Central Limit Theorem, and how does it apply here?
3. How do we calculate the z-score for proportions in large samples?
4. What would the probability of getting a proportion of less than 13% be?
5. How does increasing the sample size affect the probability distribution?

Tip:

When working with proportions, the standard error can be calculated using $\sqrt{\frac{p(1 - p)}{n}}$, where $p$ is the population proportion and $n$ is the sample size. This is key for finding probabilities using the normal distribution.