Which of the following is the probability that Z
 will be greater than 1.645
 or P(Z>1.645)
?


Question 7Select one:

a.
0.0500




b.
0.5000



c.
0.9500



d.
0.9505

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.

Which of the following is the probability that Z will be greater than 1.645 or P(Z>1.645)?

Question 7Select one:

a. 0.0500
b. 0.5000
c. 0.9500
d. 0.9505

Discover how to calculate the probability that Z is greater than 1.645 in the standard normal distribution. This question covers core statistics concepts such as probability and the properties of the standard normal distribution. Suitable for students in Grades 9-12.

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