Math Problem Statement
Solution
The problem in the image reads:
"Given the normally distributed random variable , find ."
Solution:
The random variable follows a normal distribution with mean and standard deviation . We need to find the probability .
First, we standardize the variable using the Z-score formula:
For :
Now, we need to find the probability .
Using the standard normal distribution table or a calculator, the probability for is approximately:
Final Answer:
Would you like further details or have any questions?
Here are some related questions:
- What is the probability for the same distribution?
- How do you calculate the Z-score for a value less than the mean?
- What is given ?
- How does changing the mean affect the probability ?
- Can you find for the given distribution?
Tip: When working with normal distributions, always convert to the Z-score first, as it allows you to use standard tables or tools for probability calculations.
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Probability
Formulas
Z-score formula
Theorems
Properties of Normal Distribution
Suitable Grade Level
Advanced High School / College
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