Math Problem Statement
Find the percent of the total area under the standard normal curve between the following z-scores. zequals=negative 1.3−1.3 and zequals=negative 0.75−0.75
Solution
To find the percent of the total area under the standard normal curve between the z-scores and , we can use the standard normal distribution table or a calculator that provides cumulative probabilities for the standard normal distribution.
- First, find the cumulative probability for .
- Next, find the cumulative probability for .
- Subtract the cumulative probability at from the cumulative probability at .
Using the standard normal distribution table:
- The cumulative probability for is approximately 0.0968.
- The cumulative probability for is approximately 0.2266.
Now, subtract these probabilities:
Therefore, the percent of the total area under the standard normal curve between and is .
Would you like any more details or have any other questions?
Here are 5 questions you might want to ask next:
- How do you find the area under the normal curve for any given z-score range?
- What is the significance of the standard normal distribution in statistics?
- Can you explain how to use the standard normal distribution table?
- How can we find the z-score for a given percentile?
- What are some real-life applications of the standard normal distribution?
Tip: When working with normal distributions, always sketch the curve and shade the area of interest. This helps in visualizing the problem and understanding which cumulative probabilities to use.
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Math Problem Analysis
Mathematical Concepts
Statistics
Normal Distribution
Formulas
Standard Normal Distribution Table
Theorems
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Suitable Grade Level
Advanced High School
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