Math Problem Statement

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

Solution

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

  1. The cumulative probability up to Z=1.645Z = 1.645 is approximately 0.95000.9500. This means that the probability P(Z1.645)=0.9500P(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):

P(Z>1.645)=10.9500=0.0500P(Z > 1.645) = 1 - 0.9500 = 0.0500

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

The correct answer is:

a. 0.0500


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 ZZ will be less than -1.645?
  2. How do you calculate P(1.645<Z<1.645)P(-1.645 < Z < 1.645)?
  3. What does the value Z=1.645Z = 1.645 represent in a normal distribution?
  4. How would you compute P(Z>2.33)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 ZZ-score is always less than 0.5, since half of the distribution lies to the left of zero.

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Math Problem Analysis

Mathematical Concepts

Statistics
Standard Normal Distribution
Probability

Formulas

P(Z > z) = 1 - P(Z ≤ z)

Theorems

Properties of the Standard Normal Distribution

Suitable Grade Level

Grades 9-12