Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of e so that the following is true. P(c≤250.78)-0.7456

Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

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.

Explore how to find the Z-score in a normal distribution problem where P(Z ≤ c) = 0.7456. Learn the step-by-step solution using the standard normal distribution table or calculator, including detailed calculations and explanations.

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