Math Problem Statement
Solution
The question asks for the probability from the standard normal distribution, where the mean and standard deviation .
Step-by-Step Solution:
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Locate Z = 2.23 on the Z-table, which gives the cumulative probability from to 2.23.
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From the Z-table, the cumulative probability for is:
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Answer:
Expressing the probability rounded to 4 decimal places:
This means the area to the left of under the standard normal curve is 0.9871.
Would you like further details or have any questions?
Related Questions:
- What is the cumulative probability for ?
- How do you interpret probabilities in a standard normal distribution?
- What is the probability using the complement rule?
- How do we calculate probabilities when Z-scores are negative?
- What is the total area under the standard normal curve?
Tip: When calculating probabilities for normal distributions, if Z-scores aren't integers, a Z-table or software tools (like Excel or calculators) can be very handy.
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Math Problem Analysis
Mathematical Concepts
Probability
Standard Normal Distribution
Z-scores
Formulas
Cumulative distribution function for Z-score
Theorems
Empirical Rule
Properties of the Normal Distribution
Suitable Grade Level
Grades 10-12
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