To solve for $c$ in the equation $P(c \leq 250.78) - 0.7456$, it appears there might be a misunderstanding or typo in the problem statement because typically, the standard normal distribution $Z$ is used to find probabilities, and the value $250.78$ seems unusually large for a standard normal context.

However, assuming the problem intends to find the z-score $c$ such that the probability associated with that z-score is $P(Z \leq c) = 0.7456$, we can proceed as follows:

Step-by-Step Solution:

1. Identify the Probability:
   We are given $P(Z \leq c) = 0.7456$.

2. Find the Corresponding z-Score:
   Using the standard normal distribution table (or calculator), we need to find the z-score corresponding to a cumulative probability of 0.7456.

3. Use the z-Table or Calculator: The z-score corresponding to a cumulative probability of 0.7456 is approximately $c = 0.66$.

Final Answer:

So, the value of $c$ that satisfies the equation $P(Z \leq c) = 0.7456$ is approximately $c = 0.66$.

Let me know if you would like further details or explanations! Here are five related questions:

1. What is a z-score, and how is it used in probability?
2. How do you find a z-score from a given probability using a z-table?
3. What is the significance of the standard normal distribution in statistics?
4. How would you calculate the probability for a given z-score?
5. How do you interpret cumulative probabilities in a normal distribution?

Tip: When using z-tables, always double-check whether the table gives cumulative probabilities from the left or right of the mean to avoid errors.