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≤0.78)-0.7456

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

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.

Learn how to determine the value of e in a standard normal distribution problem where Z follows the standard normal distribution. This problem involves calculating cumulative probabilities and subtracting a given value to find the result. Suitable for advanced high school students and beyond.

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