Math Problem Statement
For a standard normal distribution, find:
P(-1.99 < z < -0.23)
Solution
To find the probability for the standard normal distribution between and , you can use a standard normal table (Z-table) or a calculator. The Z-table gives the cumulative probability from the left of the curve up to a given z-value.
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Find the cumulative probability for : From the Z-table, .
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Find the cumulative probability for : From the Z-table, .
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Calculate the probability between the two values:
So, .
Would you like more details or have any questions?
Relative questions:
- What is the cumulative probability for ?
- How do you calculate the probability for a given z-value?
- What is the probability between two positive z-values (e.g., )?
- How can you calculate probabilities using a calculator instead of a Z-table?
- How do you interpret z-values in a real-world context (e.g., in height or test scores)?
Tip:
Always remember that the Z-table typically provides the area to the left of a z-value, so subtracting cumulative probabilities is key for finding the area between two z-values.
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Math Problem Analysis
Mathematical Concepts
Probability
Standard Normal Distribution
Z-Scores
Formulas
P(a < Z < b) = P(Z < b) - P(Z < a)
Z-score formula
Theorems
Standard Normal Distribution
Cumulative Distribution Function
Suitable Grade Level
Grades 11-12 (High School) or College Level
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