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.