Math Problem Statement
Solution
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Problem Statement:
Find the probabilities for each of the following given and convert into percentage form.
GIVEN:
I will now solve these problems using the Z-table and then convert them to percentages.
Let me calculate them for you.Here are the probabilities converted into percentage form:
- = 85.08%
- = 30.85%
- = 95.05%
- = 71.28%
- = 60.67%
Would you like more details on how these were calculated or do you have any other questions?
Here are 5 relative questions to expand on this topic:
- How are Z-scores calculated from raw data in a normal distribution?
- What is the importance of the standard normal distribution in statistics?
- How would you calculate the probability for a Z-value not found in a Z-table?
- What is the difference between and ?
- Can you explain why the total area under the standard normal curve equals 1?
Tip: When working with Z-scores, remember that they represent the number of standard deviations away from the mean, making them useful for comparing different data sets.
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Math Problem Analysis
Mathematical Concepts
Probability
Standard Normal Distribution
Z-Scores
Formulas
Z = (X - μ) / σ
Theorems
Standard Normal Distribution Table
Suitable Grade Level
Grades 10-12
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