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In this problem, we are asked to find the z-score \( d \) such that the probability \( P(z > d) = 0.9494 \). The z-scores are normally distributed with a mean of 0 and a standard deviation of 1, which corresponds to the standard normal distribution.

To solve this, we'll use the following steps:

1. The value of \( P(z > d) = 0.9494 \) tells us that the probability to the right of the z-score \( d \) is 0.9494. 
2. Since the total area under the normal distribution curve is 1, the probability to the left of the z-score \( d \) is \( 1 - 0.9494 = 0.0506 \). 
3. Now, we need to find the z-score corresponding to the cumulative probability of 0.0506.

Using standard normal distribution tables or a statistical calculator, we find that the z-score that corresponds to a cumulative probability of 0.0506 is approximately \( -1.6449 \).

Thus, \( d = -1.6449 \).

Let me know if you would like further details or have any questions!

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Here are 5 related questions:
1. What is the cumulative probability for a z-score of 0?
2. How would the answer change if the mean was not 0 but some other value?
3. Can you calculate \( P(z < d) \) if \( P(z > d) \) is given as 0.80?
4. What is the interpretation of z-scores in a real-world context?
5. How would this problem change if we wanted \( P(z > d) = 0.90 \) instead of 0.9494?

**Tip**: Remember that z-scores are a measure of how many standard deviations a value is away from the mean in a normal distribution.

Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > d) = 0.9494, find d.

Learn how to calculate the z-score for a standard normal distribution where P(z > d) = 0.9494. This problem covers concepts of cumulative probability, z-scores, and the standard normal distribution curve. Suitable for advanced high school or introductory college statistics courses.

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