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 , we need to refer to the standard normal distribution table, which provides probabilities for a standard normal variable .
- The cumulative probability up to is approximately . This means that the probability .
- Since the total probability under the curve is 1, we can subtract this from 1 to find :
Thus, the probability that will be greater than 1.645 is .
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:
- What is the probability that will be less than -1.645?
- How do you calculate ?
- What does the value represent in a normal distribution?
- How would you compute ?
- 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 -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