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To find the value of \( c \) such that \( P(Z > c) = 0.6915 \) where \( Z \) follows the standard normal distribution, follow these steps:

1. Recognize that \( P(Z > c) = 0.6915 \). This is the probability that the standard normal variable is greater than \( c \).
2. To use the standard normal distribution table (which usually gives the cumulative probability from the left, \( P(Z < c) \)), convert the given probability:

   \[
   P(Z < c) = 1 - P(Z > c) = 1 - 0.6915 = 0.3085
   \]

3. Now, look for the value of \( c \) where \( P(Z < c) = 0.3085 \) in the standard normal distribution table.
4. Checking the table or using a calculator, \( P(Z < c) = 0.3085 \) corresponds to \( c \approx -0.50 \).

Thus, the value of \( c \) rounded to two decimal places is:
\[
\boxed{-0.50}
\]

Would you like further details or have any other questions?

Here are five related questions:
1. How do you find a critical value for a two-tailed test using the standard normal distribution?
2. What does the value \( P(Z > c) \) represent in terms of the standard normal curve?
3. How do you convert between left-tail and right-tail probabilities?
4. What is the significance of the mean and standard deviation in a standard normal distribution?
5. How would you find \( c \) if \( P(Z < c) \) were given instead?

**Tip:** Always remember that standard normal tables typically provide left-tail probabilities (i.e., \( P(Z < c) \)). For right-tail probabilities, use the complement: \( P(Z > c) = 1 - P(Z < c) \).

Suppose Z follows the standard normal distribution. Determine the value of c so that P(Z > c) = 0.6915.

Learn how to find the value of c such that P(Z > c) = 0.6915 in the standard normal distribution. This involves converting between left-tail and right-tail probabilities and using standard normal distribution tables. Suitable for students in Grades 9-12.

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