To clarify the problem, we need to determine the value of $e$ so that $P(Z \leq c) - 0.7456 = e$, where $c = 0.78$ and $Z$ follows a standard normal distribution.

Step-by-Step Solution:

1. Calculate $P(Z \leq 0.78)$:

   • We need to find the cumulative probability $P(Z \leq 0.78)$ from the standard normal distribution table or using a calculator.
   • Using a standard normal distribution table, $P(Z \leq 0.78)$ corresponds to approximately 0.7823.

2. Determine $e$:

   • The problem asks us to subtract 0.7456 from this probability: $e = P(Z \leq 0.78) - 0.7456$ $e = 0.7823 - 0.7456 = 0.0367$

Final Answer:

So, the value of $e$ is approximately $0.04$ when rounded to two decimal places.

Let me know if you need further details! Here are five related questions:

1. How do you interpret the result $P(Z \leq 0.78)$?
2. What are cumulative probabilities in a standard normal distribution?
3. How do you use a standard normal distribution table to find probabilities?
4. What does the value $e$ represent in this context?
5. How can this method be applied to other z-scores?

Tip: Always ensure to round intermediate results accurately to avoid errors in the final answer.