To solve for $P(Z > 1.645)$, we need to refer to the standard normal distribution table, which provides probabilities for a standard normal variable $Z$.

1. The cumulative probability up to $Z = 1.645$ is approximately $0.9500$. This means that the probability $P(Z \leq 1.645) = 0.9500$.
2. Since the total probability under the curve is 1, we can subtract this from 1 to find $P(Z > 1.645)$:

$P(Z > 1.645) = 1 - 0.9500 = 0.0500$

Thus, the probability that $Z$ will be greater than 1.645 is $\boxed{0.0500}$.

The correct answer is:

a. 0.0500

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Would you like more details or have any questions on this?
Here are 5 related questions to expand on the concept:

1. What is the probability that $Z$ will be less than -1.645?
2. How do you calculate $P(-1.645 < Z < 1.645)$?
3. What does the value $Z = 1.645$ represent in a normal distribution?
4. How would you compute $P(Z > 2.33)$?
5. Can you explain the 68-95-99.7 rule in the context of the normal distribution?

Tip: The area under the normal distribution curve to the right of a positive $Z$-score is always less than 0.5, since half of the distribution lies to the left of zero.