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Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of c so that the following is true. Round your answer to two decimal places.

The problem requires finding the value of \( c \) such that the probability \( P(Z > c) = 0.7642 \), where \( Z \) follows the standard normal distribution (mean \( \mu = 0 \), standard deviation \( \sigma = 1 \)).

To solve this:

1. Since \( P(Z > c) = 0.7642 \), the cumulative probability \( P(Z \leq c) \) is \( 1 - 0.7642 = 0.2358 \).
2. Next, we need to find the value of \( c \) such that the cumulative probability \( P(Z \leq c) = 0.2358 \) using the standard normal distribution table or a calculator.

I'll find the value of \( c \) by looking up this cumulative probability.

### Calculation:
Using a standard normal distribution table or a calculator:

- \( P(Z \leq c) = 0.2358 \) corresponds to \( c \approx -0.72 \).

Thus, the value of \( c \) is approximately **-0.72**.

Would you like to know more details or have any further questions?

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**Relative Questions:**

1. What does the standard normal distribution represent?
2. How do you interpret the value of \( c \) in this context?
3. Why is the cumulative probability used to find the value of \( c \)?
4. Can you explain how to use a standard normal table?
5. What does the probability \( P(Z > c) = 0.7642 \) imply about the value of \( Z \)?
6. How would this process change if the distribution was not standard normal?
7. How do changes in the probability \( P(Z > c) \) affect the value of \( c \)?
8. What is the significance of rounding \( c \) to two decimal places?

**Tip:** When using a standard normal distribution table, always remember to consider whether you are looking for a left-tail or right-tail probability to avoid errors.

Learn how to find the value of c in a standard normal distribution problem. This involves calculating the probability P(Z > c) = 0.7642, where Z follows the standard normal distribution (mean µ = 0, standard deviation σ = 1). Detailed step-by-step solution provided.

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